Here it is, after months of blood, sweat, and toil: my ranking of all 24 unique units (UUs) in Civilization 3, including the Play the World expansion. It's a long post. Or, rather, posts... 
With a grade distribution a statistics professor would be proud of (a third of the units are above average, a third average, and a third below average), here is my grading scale:
A: Great. Has the potential to single-handedly throw the game in your favor.
B: Good. Very useful and advantageous.
C: Average. Still useful, but nothing special compared to other UUs.
D: Poor. Little or no use/advantage.
F: Terrible. A complete waste of time, money, resources, and UU slot.
Essentially, units graded B or above are my favorites, and I think these civilizations are the most fun to play. However, probably any C- or better unit has the potential to be great in the hands of a skilled player.
Since this is a ranking of units, I looked at them purely in terms of their military usefulness, not how opportune a time their triggered Golden Age is. I figured that unless a GA comes unusually early or late, its mostly a players style that determines whether its good timing or not (and if nothing else, a UUs Golden Age is useful for cranking out more UUs.). For instance, whether or not the French Musketeer triggers a better Golden Age than the Persian Immortal was irrelevant to my ranking; the Immortal is clearly a better unit. However, I was particularly harsh on units that are unable to trigger a GA (Korean Hwacha, American F-15), since building a Great Wonder to trigger GA is oftentimes a crap shoot, and if youre playing on Emperor or Deity, you probably have a better chance of winning the lottery.
Disclaimer: The beauty of a game like Civilization is the amazing breadth of unique strategies that players develop. Especially with early-game rush UUs (Aztec Jaguar Warrior, Egyptian War Chariot), one mans trash is another mans treasure, and thus my ranking criteria does not apply to everyone. I tried to rank the UUs from a general point of view without a specific strategy in mind, but undoubtedly my personal preferences played a role. A units usefulness also differs based on map size and type and the number of opponents, and my rankings are based on my experience with default (standard size) map settings and opponents. Also, these rankings dont really apply to multiplayer games, since human opponents open a whole new can of worms. :slay:
Ive listed the units in (Attack/Defense/Movement, Shield Cost) format, plus units with bombard ability also have (Bombard/Range/Rate of Fire). I have the Civ3 1.29f and PTW 1.14f patches, the latest U.S. updates as of January, 2003.
The rankings, from best to worst:
Viking Berserk (6/2/1, 70s), replaces Longbowman (4/1/1, 40s). The Berserk is powerful. Extremely powerful. Ridiculously powerful. When I first read the description of this unit, I thought there was a misprint. How could a 4/1/1 unit be replaced by a 6/2/1 amphibious unit? My only guess is that the playtesters were asleep at the wheel for this one. As it is an early Middle Ages unit, the Berserks 6 attack is by far and away the most powerful attack of the era, a full 50% more powerful than Knights (and all their UU equivalents) and Medieval Infantry. And consider this: with the exception of the Ottoman Sipahi, no unit has a higher attack value than the Berserk until Tanks. The 6 attack value alone would rank the Berserk among the better UUs in the game, but this isnt even the units most powerful feature. Its most powerful ability, amphibious attack, comes almost two full eras before Marines, the only other amphibious unit in the game. Whereas the Marines ability is balanced with (or, one might say, diluted by) the other units of its time period, the Berserks amphibious ability is an anachronism in the Middle Ages. The Berserk war party can go from port to port, pillaging and looting with impunity, while the enemys Knights and Cavalry spin helplessly in circles, since they cant attack naval units. This leaves a naval counterattack as the only option, but until the advent of the Destroyer, naval units attack and defend equally, so naval superiority is merely a matter of possessing the most ships. This means that for the Vikings, a stack of naval units loaded with Berserks and guarded by empty Galleys/Caravels/Ironclads (depending on the era) is all but invincible.
To top it all off, the Berserk has an additional point of defense over the Longbowman, and requires no resources to build. This is just icing on a mammoth wedding cake. Okay, the Berserk expensive, but it costs the same as a Knight, which means it isnt exactly going to cripple anybodys Middle Age economy. Grade: A+
Persian Immortal (4/2/1, 30s), replaces Swordsman (3/2/1, 30s). The Ancient Era Immortal, just one technologys worth of research for the Persians, could easily go by a different name: the Medieval Infantry. Compared to the Medieval Infantry, the Immortal has identical stats, is cheaper, and appears an entire era earlier.
This grants the Persians a medieval attack force in the Ancient Era, an edge that is often crucial in the early game. The Immortal, which attacks on par with a Knight, continues to be effective through the end of the Middle Ages. Through heavy use of the Immortal, the Persians can easily gain an early lead and never look back. Grade: A
Iroquois Mounted Warrior (3/1/2, 30s), replaces Horseman (2/1/2, 30s). Ive always been a big fan of the Mounted Warrior, a unit which was single-handedly responsible for my first few Deity victories. :worshp: I used to think of them as Swordsmen with 2 movement, until PTW introduced the Gallic Swordsman, which literally is a Swordsman with 2 movement. Stacks of Mounted Warriors, complete with retreat capabilities, can be terrors of the Ancient Era. Indeed, I found them to be effective through at least half of the Middle Ages. Grade: A
Ottoman Sipahi (8/3/3, 100s), replaces Cavalry (6/3/3, 80s). The Sipahis 8 attack, which is 25% greater than any unit until Tanks, makes for one hell of an offensive unit. The Sipahi are absolutely deadly against Medieval Era units, effective against Riflemen/Guerillas, and can even be used to good effect against Infantry
, the unit which ordinarily signals the beginning of the end of Cavalry. I was torn between this and the Mounted Warrior for the last "A" ranking, and only the Sipahis high cost (the same as a Tank!) turned the tide, though I would still trade five Cavalry for four Sipahi. Grade: B+
Greek Hoplite (1/3/1, 20s), replaces Spearman (1/2/1, 20s). The Hoplite is basically a cheap Pikeman that doesnt require iron and is available an entire era earlier. Only fools and Persians would invade Greece in the Ancient Era. Their cheap cost also makes them plentiful and efficient. In terms of cost, Hoplites are more effective defenders than Legions, Numidian Mercenaries, Pikemen, and even Musket Men!
Cost-compare a Hoplite, with 3 defense for 20 shields and no resource requirements to a Musket Man, with 4 defense for 60 shields and saltpeter. Unless you want to save on unit upkeep money, the Hoplite is clearly the better choice. Thus, the Hoplite, which is available from day one for the Greeks, has the potential to be used effectively all the way to the Industrial Era. Grade: B
Roman Legionary (3/3/1, 30s), replaces Swordsman (3/2/1, 30s). At first glance, the Legionary seems to be quite an impressive unit. It essentially combines the attack of a Swordsman with the defense of a Pikeman. Once iron is secured, the Romans need not build anything other than Legions until the Middle Ages, and can create an attack force that is difficult to counterattack. However, this theoretical advantage isnt that strong in actual gameplay, since attacking in the Ancient Era proves to be more important than defending, and the Legionarys extra defense isnt called into play as often as one would think. You dont want to start the game next to Rome, but being them yourself hardly makes you unstoppable. Grade: B
Chinese Rider (4/3/3, 70s), replaces Knight (4/3/2, 70s). Mobility is often the key to victory, and no unit embodies that more than the Rider. While an extra movement point for an already mobile unit might not seem like much, the 50% increase does wonders for attack position, resource denial, and flexible homeland defense. Use Riders for a while and standard Knights will seem maddeningly slow in comparison. Grade: B
Japanese Samurai (4/4/2, 70s), replaces Knight (4/3/2, 70s). A great multi-purpose unit, the Samurai does it all. Its mobile, it attacks as well as a Knight, and defends as well as a Musket Man while preventing retreating. The Japanese need not build any unit other than Samurai for a long time. The only drawback is that sometimes you dont want your Samurai to be the primary defender in a stack, but it usually gets picked by default because its the strongest. As an added bonus, though, the Samurai has cool animation and sound.
Grade: B
Continued...

With a grade distribution a statistics professor would be proud of (a third of the units are above average, a third average, and a third below average), here is my grading scale:
A: Great. Has the potential to single-handedly throw the game in your favor.
B: Good. Very useful and advantageous.
C: Average. Still useful, but nothing special compared to other UUs.
D: Poor. Little or no use/advantage.
F: Terrible. A complete waste of time, money, resources, and UU slot.
Essentially, units graded B or above are my favorites, and I think these civilizations are the most fun to play. However, probably any C- or better unit has the potential to be great in the hands of a skilled player.
Since this is a ranking of units, I looked at them purely in terms of their military usefulness, not how opportune a time their triggered Golden Age is. I figured that unless a GA comes unusually early or late, its mostly a players style that determines whether its good timing or not (and if nothing else, a UUs Golden Age is useful for cranking out more UUs.). For instance, whether or not the French Musketeer triggers a better Golden Age than the Persian Immortal was irrelevant to my ranking; the Immortal is clearly a better unit. However, I was particularly harsh on units that are unable to trigger a GA (Korean Hwacha, American F-15), since building a Great Wonder to trigger GA is oftentimes a crap shoot, and if youre playing on Emperor or Deity, you probably have a better chance of winning the lottery.

Disclaimer: The beauty of a game like Civilization is the amazing breadth of unique strategies that players develop. Especially with early-game rush UUs (Aztec Jaguar Warrior, Egyptian War Chariot), one mans trash is another mans treasure, and thus my ranking criteria does not apply to everyone. I tried to rank the UUs from a general point of view without a specific strategy in mind, but undoubtedly my personal preferences played a role. A units usefulness also differs based on map size and type and the number of opponents, and my rankings are based on my experience with default (standard size) map settings and opponents. Also, these rankings dont really apply to multiplayer games, since human opponents open a whole new can of worms. :slay:
Ive listed the units in (Attack/Defense/Movement, Shield Cost) format, plus units with bombard ability also have (Bombard/Range/Rate of Fire). I have the Civ3 1.29f and PTW 1.14f patches, the latest U.S. updates as of January, 2003.
The rankings, from best to worst:
Viking Berserk (6/2/1, 70s), replaces Longbowman (4/1/1, 40s). The Berserk is powerful. Extremely powerful. Ridiculously powerful. When I first read the description of this unit, I thought there was a misprint. How could a 4/1/1 unit be replaced by a 6/2/1 amphibious unit? My only guess is that the playtesters were asleep at the wheel for this one. As it is an early Middle Ages unit, the Berserks 6 attack is by far and away the most powerful attack of the era, a full 50% more powerful than Knights (and all their UU equivalents) and Medieval Infantry. And consider this: with the exception of the Ottoman Sipahi, no unit has a higher attack value than the Berserk until Tanks. The 6 attack value alone would rank the Berserk among the better UUs in the game, but this isnt even the units most powerful feature. Its most powerful ability, amphibious attack, comes almost two full eras before Marines, the only other amphibious unit in the game. Whereas the Marines ability is balanced with (or, one might say, diluted by) the other units of its time period, the Berserks amphibious ability is an anachronism in the Middle Ages. The Berserk war party can go from port to port, pillaging and looting with impunity, while the enemys Knights and Cavalry spin helplessly in circles, since they cant attack naval units. This leaves a naval counterattack as the only option, but until the advent of the Destroyer, naval units attack and defend equally, so naval superiority is merely a matter of possessing the most ships. This means that for the Vikings, a stack of naval units loaded with Berserks and guarded by empty Galleys/Caravels/Ironclads (depending on the era) is all but invincible.

Persian Immortal (4/2/1, 30s), replaces Swordsman (3/2/1, 30s). The Ancient Era Immortal, just one technologys worth of research for the Persians, could easily go by a different name: the Medieval Infantry. Compared to the Medieval Infantry, the Immortal has identical stats, is cheaper, and appears an entire era earlier.

Iroquois Mounted Warrior (3/1/2, 30s), replaces Horseman (2/1/2, 30s). Ive always been a big fan of the Mounted Warrior, a unit which was single-handedly responsible for my first few Deity victories. :worshp: I used to think of them as Swordsmen with 2 movement, until PTW introduced the Gallic Swordsman, which literally is a Swordsman with 2 movement. Stacks of Mounted Warriors, complete with retreat capabilities, can be terrors of the Ancient Era. Indeed, I found them to be effective through at least half of the Middle Ages. Grade: A
Ottoman Sipahi (8/3/3, 100s), replaces Cavalry (6/3/3, 80s). The Sipahis 8 attack, which is 25% greater than any unit until Tanks, makes for one hell of an offensive unit. The Sipahi are absolutely deadly against Medieval Era units, effective against Riflemen/Guerillas, and can even be used to good effect against Infantry

Greek Hoplite (1/3/1, 20s), replaces Spearman (1/2/1, 20s). The Hoplite is basically a cheap Pikeman that doesnt require iron and is available an entire era earlier. Only fools and Persians would invade Greece in the Ancient Era. Their cheap cost also makes them plentiful and efficient. In terms of cost, Hoplites are more effective defenders than Legions, Numidian Mercenaries, Pikemen, and even Musket Men!

Roman Legionary (3/3/1, 30s), replaces Swordsman (3/2/1, 30s). At first glance, the Legionary seems to be quite an impressive unit. It essentially combines the attack of a Swordsman with the defense of a Pikeman. Once iron is secured, the Romans need not build anything other than Legions until the Middle Ages, and can create an attack force that is difficult to counterattack. However, this theoretical advantage isnt that strong in actual gameplay, since attacking in the Ancient Era proves to be more important than defending, and the Legionarys extra defense isnt called into play as often as one would think. You dont want to start the game next to Rome, but being them yourself hardly makes you unstoppable. Grade: B
Chinese Rider (4/3/3, 70s), replaces Knight (4/3/2, 70s). Mobility is often the key to victory, and no unit embodies that more than the Rider. While an extra movement point for an already mobile unit might not seem like much, the 50% increase does wonders for attack position, resource denial, and flexible homeland defense. Use Riders for a while and standard Knights will seem maddeningly slow in comparison. Grade: B
Japanese Samurai (4/4/2, 70s), replaces Knight (4/3/2, 70s). A great multi-purpose unit, the Samurai does it all. Its mobile, it attacks as well as a Knight, and defends as well as a Musket Man while preventing retreating. The Japanese need not build any unit other than Samurai for a long time. The only drawback is that sometimes you dont want your Samurai to be the primary defender in a stack, but it usually gets picked by default because its the strongest. As an added bonus, though, the Samurai has cool animation and sound.

Continued...