I've played Civilization 4, and I thought it was a great game. I'm thinking of buying the new one (Civilization 5), but I thought I'd get an opinion from someone who's played the game.
Civ 5 is a bit different from the rest in the series, and I keep seeing posts in forums from fans who are pissed off about that.
Personally, as a lifelong Civ fan (I think I still have all the floppies for the first one), I like it.
Couple of things you might want to consider, if you haven't already:
Hex grid - No more squares, everything's on hexes now.
Unit Stacking - Whereas before you could put more than one unit in the same square, thus building yourself a stack o' death, you can't do that anymore. It makes the combat a little more involving; you can't just keep spamming units all over the place. On the other hand larger armies can be a bit cumbersome to wield.
Streamlined Interface - The new Civ is a lot sleeker, taking a few ideas from the Xbox version where they had to slim it down a bit. I personally didn't mind the interface in Civ 4. I can see that the new one is a bit more user friendly and all the information is still there and there are a few welcome additions to make navigating your empire a little easier.
Policies - Tweaking your government has changed a little. Instead of what you would've seen in 4, you choose from a tech tree-like 'social policy' system of various ways to help you civ grow. I'm a ig fan; it gives you much more freedom in choosing what your civ is good at and refining your victory strategy.
Can't think of any more right now. There's no way you could mistake it for anything other than a Civ game anyway, so if you liked the last one, this one shouldn't disappoint.