Given that it's a game that's slowly consuming my soul (even though I've only clocked up 23 hours in the last week, which is far less than some) I figured I'd post some thoughts about it on here.
The first thought is that it actually runs surprisingly well on my laptop. Sure, I'm using the lowest settings and it still runs my CPU pretty much to the limit, but I've not had any of the issues other people seem to have had. It's crashed on me a grand total of one time so far, which is far less than what some people with certain graphics cards have been reporting. I've been using the Dx9 version but I don't really have a choice because I'm on XP and it doesn't have support for Dx10 and above.
That said, my use of it hasn't been entirely bug-free (click to enlarge):
The other thing I know a few people have complained about is that late-on in the game you have to wait ages for the AI to take its turns. I've not really experienced this that badly, but the largest map I've used so far is "small", which is the third largest out of the six options, and turns started to take a noticeable amount of time late-on in the game and I could see how it'd easily scale up to be quite a long amount of time on the large maps with lots of AI players.
I've had a few games now and I'm starting to get a decent feel for the basics and some of the more advanced options to control. I've been going for a few Steam achievements, mostly playing as different maps and civs and going for different victories, which I think is a pretty good way to get a proper feel for the game and the best style of play.
For conquest victory (wipe out all the other players), it seems pretty standard. My main thought on it in comparison to Civ II is that against decent players you almost certainly have to be relentless and focused in attacking other people. This is mostly from the perspective that I think with some resilient opponents it'll be fairly challenging to win a conquest victory before someone swoops in with a science or culture one.
The science victory (win the space race) I like, and I feel it's a fairly easy one. The thing with focusing on advancing science is that you obtain all the upgraded units and buildings more quickly than your opponents, which makes defending yourself from attack a fair bit easier because you have the superior force technologically, even if your opponent might have more units with more experience. I also don't think that unit/building production really hinders your science progress that much either, so it's not like you can't generate a fairly large army and a shitload of science at the same time (thought getting the money to support it might be a different issue).
The culture victory is reasonably straightforward. You generate culture points, these points allow you to unlock social policies which provide various benefits. If you complete enough policy trees (five, which equates to twenty-five policies) then you can build the Utopia Project wonder that'll win a cultural victory for you. It's not, in my single-game experience of it, a particularly tough one to go for, again because your military tactics don't really affect culture production that much. However, each extra city increases the social policy cost by 30%, meaning that once you've got four cities it's no longer beneficial towards victory to build more cities (ignoring other benefits that extra cities have). You can still expand by taking over enemy cities and making them puppet states, which don't have the policy cost, but I still don't really like the cultural victory path because my preferred style of play is to create a huge, sprawling empire, which basically makes it impossible. Still, if people don't mind small, heavily fortified empires then I could see why they'd go for this.
Diplomatic victory I just don't seem to understand. I could just suck at Diplomacy, but I don't know why anyone would bother going for this as it seems by a mile to be the most difficult one. You can't get it until the United Nations has been built, so by the time you can go for it, it'll be fairly late-on in the game and other people will presumably be close to other victories. The main issue with it from what I've seen is just the number of votes you need from all the other civs and city states to win it. The one game I even paid any attention to it, by the time I looked at it the majority of the city states had been wiped out, and 9 votes were required to win it with only 8 votes possible, which by my understanding meant it was impossible to win unless I went around and liberated all the city states, which would have been a pretty big effort. Plus that would mean declaring war on plenty of civs which would presumably hurt the number of votes I'd be able to get in other ways.
Still, it's a good, addicting game from what I've played so far, and I definitely feel like it's got absolutely tons more hours left in it.