Overall I am fairly disappointed. I've been a massive fan of the series since the very first game, and I don't even want to think about the amount of hours I've spent playing Civ4 the past few years (it's terrifyingly high).
First, the positives. It is quite nice looking, though not as good as I expected. Unit animations are fantastic, particularly when ships fire their guns. Watching the canons going off on a Ship-of-the-Line is beautiful. The soundtrack is brilliant. The guy who does the narrations is no Leonard Nimoy, but does a good job.
However Civ5 just isn't hitting the spot. I'm already tiring of playing it. I'm probably going to go back to Civ4. The main reason, the main thing I just can't get over, is the 1 unit per tile thing. It just doesn't work. Movement is so restrictive it just becomes tedious managing an army and having units dotted all over your farmlands because you can't put them in to cities is annoying. You can't move onto the same tile as an allied unit either, leading to ridiculous traffic jams all the time. If an ally fills up an area of land with units and you don't have a unit with enough movement points to pass through them in one go, you won't be going anywhere any time soon. A much better idea in my opinion would have been to have had a unit limit per tile, say 4 per tile. This would stop the large stacked armies issue from Civ4 and stop the issues I have with Civ5.
Another thing which, while it may seem small, has rather ruined the game somewhat for me, is the embark feature. Any unit can simply move on to a water tile and abracadabra, it turns into a boat. No more transports. This is just stupid. Once a unit is at sea it can't be stacked with warships for protection, meaning that if you really need to protect it you need 6 ships to surround it in order to protect it, and even then it can be killed by multiple bombardments anyway. Massive seaborne invasions are, while possible, not fun any more. Once you embark more than a few units things get clogged up on the high seas pretty quickly and defending them effectively on their way over is almost impossible.
Great people are not as useful as in Civ4 and I don't really care much when one appears any more.
I for one enjoyed the religion aspect of Civ4. It's a shame they removed it completely. And while I didn't use espionage or corporations much, it's still a shame that they feel its a good thing to remove such options. This is the issue with Civ5, everything has been dumbed down. Economy and science research are not as customisable either, in fact it's basically all automated. Gone are the sliders of old.
Another major problem for me is AI Civilization growth. AI Civs grow at a laughably slow rate, and seem to stop expanding all together at some point, so on a huge map the game always ends up with vast tracts of unoccupied land.
City states, while an interesting addition, now just annoy me. Luckily you can choose not to have any in the custom game options.
There are too many gripes for me to enjoy the experience. Some of the issues I have could be fixed with patches and hopefully some good mods somewhere down the line (the only reason I still play Civ4 so much is the Diversica mod - which adds huge amounts of content to Civ4, probably why I'm having so much trouble adjusting to the simplicity of Civ5). However the underlying game mechanics such as 1 unit per tile will not change, except maybe if some clever mod types are able to do it.
I'm sure this Civ will be great for people new to the series, but for many hardened Civ,Civ2,Civ3,Civ4 players like myself, it just doesn't cut the mustard. I think Civ4+Diversica mod will be reining supreme for another few years for this Civ fan.