I notice everyone is mentioning the Great Library. I normally don't make it a priority in my games, unless I'm going for a science victory. Should I be going for it more often? Also, could someone give me some pointers for the early game? Like, what do I do first - build an important wonder or get my second city up?
P.S. - I notice the AIs always create Great Works; even civs that don't go for culture victories, ever (like the Mongols). Is there logic behind this, or is it just typical AI stupidity?
The great library can be fantastic if you manage to build it, which according to other people is still very doable on king, make sure you can spend the free tech on something good, I personally tend to go for philosophy, so make sure you have the prequisite techs for it before it finishes, getting philosophy early also means an early national college, which should send your science skyrocketing even more (make sure you have a library in all your cities, and don't found a city while it's still building).
Build order wise, unless you're playing archipelago, always start off with a scout, possibly even 2 if you're playing Shoshone or are on a large pangea map or such that requires a lot of scouting and has a lot of ruins.
Then get a worker or a settler, I usually go for a worker first, then cut down forests while building the settler to speed it up significantly (make sure you have mining so you can chop forests).
If you're planning on getting the great library, start that after the settler, just get a normal library if not, if you need a couple turns to finish the technology, temporarily build something you're gonna get anyway, like a granary, switch over to the GL and then finish the granary afterwards.
Make sure you save your cash until you have enough for another settler, I usually get my 2nd settler this way, although money from CS, ruins, selling resources and such influences this a lot, buying settlers is better then building them, your city won't grow when you're building settlers.
After that it all depends on what direction you want your game to go, if you want to hoard wonders, I'd advice the Oracle, Temple of Artemis if you still can and want to go for more or a science then social policy approach, otherwise, work boats, archers, shrines or even settlers, whatever your situation demands, you also might want to get a monument somewhere early on if you're not planning on using traditions legalism for it (which I strongly advise you to do, at the moment tradition is hands down the best early game policy choice).
The main points about the great works of writing got explained already, but I'd like to add that it gives extra XP (10 IIRC) to units built there, which makes the mongol horde creating them make a lot more sense.