So far Ancient and Industrial are way out in front with Modern strolling in 3rd and Medieval barely mentioned.
This fascinates me because I would put Industrial way out last and Medieval in second.
Why?
Firstly, because I've played lots of Archipelagos where the game tends to end at 2050 about half-way through Industrial, so a lot of my games don't even have that era, let alone modern.
Secondly, all the ages have great wonders to race for, for one reason or another, all except the Industrial age. The only remotely exciting one is Darwin to jump to Hoover. That's hardly piquing my interest.
Thirdly, there are no exciting ground units, cavalry is attainable one third of the way through medieval and the next attacking unit is tank, right at the tail end of Industrial. As are the aeroplanes and big boats. Infantry is nice but it's primarily defensive.
Fourthly, communism/fascism/espionage, don't waste my time... and medicine to sanitation just to get a hospital? Imagine if Aqueduct had it's own tech, that'd drive people nuts. Then there refining and steel, the big slow-down for nothing but a very quickly outmoded boat. Yawn.
Fifthly, Pollution. THE most annoying trait of civ3 kicks in. I often try to avoid the need to go above size 12 and also try to avoid production enhancements just so that I don't have to bother shifting 5 billion workers everywhere every move and keep going in and out of city screens just to put a citizen back to work. Even with a fully railroaded nation it still irks like crazy.
Sixthly, if you're going for a culture win it's like a desert of pain, nothing, nada, zip. Only to be teased by research labs way too late in the game in the next era.
Seventhly, Ironclads? Do they really deserve a tech?
Railroad is fun though.
Whereas:
Medieval is the beginning of awesome.
Firstly, it has THE most awesome wonders. Pretty much all of them have some genuine use, and there's just so many of them.
Secondly, it kicks you off with Medieval Infantry, then gives you Knights almost the next go, then a few turns later you get Cavalry. If all that doesn't get you over someone's border nothing will.
Thirdly, this is where the big culture and trade buildings arrive and you can start to get comfortable with your impressive size 12 with it's tightly packed gold and beakers - cathedral, university, bank, economics and production getting to a steady and adequate 20 per turn with zero pollution.
Fourthly, finally putting your workers to rest for a while, all tiles maximised (for smaller nations that is) finally enabling luxury trading with pretty much all the other civs. Also, the ability to trade world maps and getting the 'big reveal'.
Chemistry, physics and printing press suck though. And Democracy's a bit meh.
So, for me, it's got to be:
Ancient
Medieval
Modern
Industrial