Setting aside the first-tier techs (fishing, the wheel, etc.)...
-Sailing unlocks coastal trade and river trade. This helps you keep an early land-grab (whether rush or REX) in the green long enough to unlock later techs, which can give you a won game. It also unlocks GLH, which on some maps (particularly tiny-islands archipelago) is horribly strong. So it's a great tech for an island-hopping or coastal-hugging REX early to grab enough land for victory.
-Pottery unlocks granaries and cottages. Enough's been said about the possibilities of cottage spamming and use of the granary to double your whip efficiency. Amongst other potentials, several cities with granaries can make a late-ancient or early-medieval rush to absolutely over-run their continents, leading to a crashed economy (which cottages can help you come from) but an unbelievable land advantage.
-If you're planning a chariot rush, you'd better get AH pretty quickly. That's about all I can think of for it as a critical tech in it's own right, although it unlocks other important options later.
-Archery. On lower difficulties you can archer-rush; I guess if you were Babylon or Mali you might make good use of it on higher ones. Also, extremely important for pre-gunpowder defense if you have a high-difficulty map where you don't get any strategic resources (horses, copper, iron, ivory).
-Meditation/Polytheism can let you found a religion, which can be key especially for an early cheesy AP victory, and also provides "free" happiness, culture, and potentially gold with a shrine. Also, the ToA (polytheism) can be extremely powerful if you're planning on also grabbing GLH. I don't consider either of these techs potentially "game-winning" ones except in the most bizarre of circumstances, but they certainly can be valuable ones.
-Masonry helps unlock GLH (mentioned before with sailing); it also gives the ability to build quarries, which can make it much easier to grab early wonders if you have the appropriate resource... to the point where you can get a massive lead in power simply by building two wonders to every else's one. And that doesn't even consider Pyramids, which is incredibly powerful for unlocking early Representation (+3 happiness in largest cities, +3 beakers per specialist)... which makes a terrifying specialist economy possible if you know what you're doing. Oh yeah, and Great Wall, which is a fairly cheap wonder which nonetheless makes you nearly immune to barbs, letting you REX far faster than normal, and gives you 2 great-person points for great spies, which is absolutely spectacular for getting an espionage economy off the ground.
-Horseback riding unlocks the Horse Archer rush. Try a highlands/Mongols map with horse-archer rushing, and come back; you'll know just how powerful HA are then. Great in situations where you couldn't chariot rush (maybe a timing issue, or bad luck in neighbors), are cramped for space by neighbors, and really want to kill things.
-Priesthood unlocks Oracle; there are some truly frightening Oracle slingshots out there, but to consider... Oracle -> CoL gives you courthouses early, which launches a powerful espionage economy while simultaneously helping you expand much more aggressively. Oracle -> Civil Service unlocks early Bureaucracy (which can let your capital dominate the world until ~1000 AD practically by itself if you have a good one; hopefully by then you're managed to secure some other good city sites...), and farms spreading irrigation (which can make city sites workable much earlier than otherwise). Oracle -> Theology founds early Christianity and lets you go for an AP win quickly. There are lots of others, but a free technology at the right time can be very powerful, so Oracle is a powerful wonder... which makes Priesthood a powerful tech.
-Monotheism unlocks Organized Religion, which is certainly one of the best civics in the game - if you're in a peaceful period, most of your cities may be building infrastructure, so that's close to +25% production in all cities with your state religion. The benefits really pile up over time. It also founds a religion if you missed Hinduism + Buddhism, can't conquer a holy city, and your game plan really calls for one.
-Bronze working. Unlocks axe rush, allows chopping, allows slavery. Three of the most powerful options a player has in the game, all for one low price. 'Nuff said.
-Writing. Critical for a specialist economy or a trade economy, as open borders are required for foreign trade and libraries are the easiest/earliest way to run scientist specialists.
-Metal Casting. The Forge is a mighty building (especially if you have gold/gems resources); the Colossus is generally good but on some maps truly overpowering (e.g., a financial civ with colossus gets 4 commerce from coastal tiles, compared to 2 commerce for everyone else). I think someone mentioned this somewhere before, but if you can get Colossus as Dutch on a water map, you've basically secured victory.
-Iron Working. Setting aside the issue of Praetorians for Rome, the swordsman rush is a good fallback if you can't pull off an axe rush. Revealing Iron is great if you didn't find copper or horses, as you really want at least one of those three resources early on in the game. And finally, the ability to chop jungles is a game-changer in some starts, if you're in danger of getting boxed in and need to expand aggressively into jungles early to keep the computer from cutting you off.
-Aesthetics. Parthenon is absolutely great for a specialist economy (especially if you have marble, and/or are not Philosophical). Similarly, Shwedagon Paya can give you early Pacifism, which is equally useful for SE. Finally, but certainly not least, this is one the techs the AI is least likely to get, which makes it an invaluable trading tool for picking up other techs in exchange from the AI.
-Mathematics significantly boosts the output from chopping, which (if you've planned for it) can make a medieval war much more practical and less costly. Another one I don't really consider potentially game-winning on it's own, although the techs it makes available are sufficient to often make it a priority anyways.
-Alphabet. Obviously if you're running an espionage economy early you want spies as soon as possible, which makes this important. More generally, though, aggressive tech trading is generally the only way to keep up with the AI early above Monarch or so difficulty, making either getting this tech yourself or trading for it critical.
-Monarchy unlocks winery plus hereditary rule. Combined, those can supply very significant increases in your happiness cap if cities, and larger cities = more production, more commerce, and generally more power.
-The Harbor, from Optics, is a very nice option for a trading economy, and the health boosts are also good. This is another tech which really isn't usually potentially game-winning by itself though, but it's position on the path to Optics and Astronomy makes it frequently worthwhile anyways (or, of course, if you're Carthage).
-Literature for Great Library and National Epic, which will let you absolutely spam great scientists early. Also, Heroic Epic, which is one of the most important national wonders as it effectively doubles the productiveness of one of your cities, which should henceforth focus almost entirely on producing military. Combined, these can let you out-tech and out-number your opponents for quite a while.
-Calendar lets you work all those Calendar resources, which can be a big boost in some starts - enough to change you from a marginal power to world-super-power status in maybe two dozen turns. It also unlocks Museum of Mausollos, which isn't usually that great at the time, but can become increasingly powerful later in the game (as empires grow larger, and great people start being more useful for starting golden ages). In fact, in some circumstances it's worth grabbing Calendar just to grab the Museum with the expectation that later in the game you'll be generating enough golden ages for that to turn the tide for you.
-Construction unlocks Catapults and Elephants. If you have Ivory, that's enough to take out any nearby opponent. If you don't have Ivory, then catapults are still critical for pre-trebuchet medieval warfare.
-Currency's +1 trade routes per city is generally worth effectively +1-2 commerce per city at the time you get it, which is nice but generally not game-breaking. The ability to build wealth can help you salvage a badly crashed economy, turning a large, poor empire into a dominant force quickly. Markets are great - increased happy cap and increased income? Yes please! Last but not least, gold trading via diplomacy is likely to earn you a few dozen to a few hundred gold per trade for the rest of the game if you're smart about it, lets you get more out of post-war ceasefires if you've been winning the war, and lets you ask your friends for gifts of gold.
-Machinery unlocks Crossbowmen, and also often Macemen. Setting aside the power of the Cho-Ko-Nu (which often makes this a beeline target for the Chinese), crossbows and maces are a significant upgrade on swords and axes. This unlocks a nice timing war before opponents get gunpowder but after longbows and axes are making it tough going invading without a boost of some sort.
Let's see... that's 24 of the first techs, and of them I can think of situations in which 20 of them are game-winners. And that doesn't even consider the situation where you want them as part of a beeline to a different tech. I think I'll stop now, because frankly most of the rest of the techs are like this too.
I think that's why people are finding it so hard to answer your question here. You have to judge your civilization, your leader, your terrain and resources, your current (and projected future) territory, the victory condition you're trying for, and your neighbors before you can say whether a given technology is going to be very important in a specific game.