So far I've got no further than the early ADs (recently started a second game after my first ended in the conquering of my capital by the Ottomans after all the green modifiers with everyone and lack of wars had lulled me into letting my guard down).
Leader: Pacal the Great (Maya)
Difficulty: Emperor
Map: Random
Size: Random
First things first:
Graphics and interface: Not a fan of the new opening animation, but I do like the fact that hitting 'Esc' now cuts past it immediately - okay it leaves the loading screen up longer, but even the old intro movie (which I loved) got boring. Also not a fan of the main screen background, but you only have to look at it while loading the game! The baroque columns etc., which hadn't really been noticeable in the preview shots, are a bit obtrusive and jarring with the standard Civ V interface look.
Civilizations: First impression was that none of the abilities much appealed. Taken in context with their UA and UB, the Maya at least turn out to be very distinctive in-game - although I expect Pottery will now be the go-to tech at the start of the game for everyone, not just the Maya, not needing to bother with Archery immediately is a bonus, as is getting what is probably the game's cheapest military unit. The Pyramid is a ridiculous upgrade to the Shrine - not just doubling its effect, but adding +2 science, all on a building cheaper than the granary.
So far my only experience with other civs from G&K has been meeting Carthage (who I've had no relations with) and Attila. I'm the kind of purist who didn't like the idea of the 'not a real civ' Huns being introduced, but psychologically it's great running into them - "Oh no, the Huns are my closest neighbours". "Wittenburg wants me to denounce the Huns. Hmm, how suicidal am I feeling?" - it would be a bit pointless from a design perspective, but for flavour I wonder if Civ should have 'non-player civs' that can't be taken by players but are in the game to represent peoples important enough historically to be represented, but who don't fit the 'civ' criterion? The psychological impact of the Huns will wear off if they continue to play in this vein: Attila is low-scoring; despite the fact that I did indeed denounce him and he's coveted my lands from the start he's spent the game just shouting at me about barbarian invasions without doing anything, and may not even have any horses.
Diplomacy: Some of the green modifiers are a nice touch, as are notifications such as "You kept your promise to the Ottomans not to expand" (although that appears to have no attendant modifiers). "We have no shared borders" is a good default positive that makes the AI more likely than previously to remain peaceful. Wars seem to be infrequent and, when I did declare one, Catherine made a reasonable peace offer - offering me peace and a token sum of gold when I wasn't particularly close to her territory, rather than demanding everything I had, when she was having to fend off the Ottomans. I did get the warmonger penalty just for that war dec (which was intended to help my relations with the Germans and Ottomans, but since I never attacked I didn't get the 'common enemy' bonus), and didn't notice it wearing off, but it also didn't result in chain denunciations (indeed the AI didn't seem to go for denunciations in that first game).
EDIT: Some of the old oddities exist. When Catherine made peace, she defaulted to Friendly with the tooltip "There have been no events that have affected relations between you" - firstly, doesn't a war count? And secondly, even if not shouldn't she then default to neutral unless she has a thing for guys in bizarre headgear? At least peace treaties no longer appear to count as a favourable trade.
I think Open Borders is probably now later than it ought to be in the tech tree - I do however like embassies as an idea, and moving RAs to Education makes the early game last longer. If I have a diplomacy complaint it's that diplomacy now feels too passive, as in Civ IV - you can more or less get by ignoring it since most of the time you won't get negative modifiers unless you actively try and annoy people, and will usually stay onside with them. But this may be an artefact of the game stage - it felt as though I was going a long time without wars, but then the early game is now longer with slower tech times (and the Ottomans just go to show I can't rely on peace indefinitely). I didn't get any particular feel for the personalities of the civs under the new AI, but again I'd need to complete several games to judge that.
City-States: The new types are nice, although being the first to find a religious city-state arguably gives too much of a bonus (double faith as well as gold - in my new game meeting Wittenberg gave me 8 faith straight away), and faith generally is more valuable than a similar amount of culture since it's a resource you can spend, and so do more with the more you've got. It just so happens that Siam is my favourite vanilla Civ V civ, and already generally regarded as one of the game's strongest; double faith from CS friends may turn out to be much, much more than a minor change to the UA. Happiness from mercantile states was something I didn't notice until I lost it, but also good. Multiple quests and the expanded types are good, and in some cases add character ("Wittenberg is bankrupt"), but CSes still play in basically the same way and I haven't noticed a difference in the use of gold (I was able to buy influence with Belgrade while allied with them, for instance). I haven't tried demanding tribute from them, though. Pledge to Protect now actually works as an option, but for some reason I no longer get notifications when I'm a friend or ally with a CS, which would be good to have back.
Combat: Combat is slightly slower under the new system; mostly this just seems to make it easier for me to extricate my units before they die, with scouts now being pretty resilient due to their fast movement and the difficulty in one- or two-shotting units. Mostly I've just fought isolated barbarians, though. Barbarian AI is if anything worse - although the AI will now move damaged units out of trouble, it still won't retreat with barbarian archers, it still attacks over rivers and wanders around cities getting shot, and archers will often not fire back without any reason not to. Losing the ranged attack on galleys also makes them easier to deal with. The changes to the combat system do however made ranged garrisons less effective, since it takes more shots to score a kill and even a slight tech advantage (spearmen rather than warriors) noticeably reduces the damage archers deal, so barbarians wandering near your cities are still a nuisance, and the AI does seem better at using them to pillage or pick off stray workers, much as it did in Civ IV.
My only wartime experience so far is with the Ottomans, who gathered a large army outside Chichen Itza before attacking - having seen it there I was moving my Swordsman to relieve the city, and that was when the Ottomans declared war, surrounded the Swordsman, and shot it to pieces. They then ignored Chichen Itza to move on Palenque rather than giving me the chance to re-arm - that attack was executed well with Warriors attacking and ranged behind, and with the AI only attacking with units likely to survive the attack (the Ottomans lost no units in that brief war). This is one instance, and Civ V AI can play wars surprisingly well on occasion so it may not be typical (one of the best-executed vanilla Civ V attacks I've faced was from the Ottomans), but the combination of a sensible unit mix (catapults and composite bows do a lot of damage), good target selection (Chichen Itza wasn't very valuable, nor was it a threat, despite being closer to Ottoman territory - possibly being a holy city made them prioritise Palenque) and a combat system that now makes it very hard for a pop 7 city with a garrison unit to kill even one attacking unit when hit by several at once definitely helped the AI.
Tech tree: Slower teching makes for an interesting early game; as above the changes to when certain diplomatic options become available will change the way the game plays. The dominance of religion makes that tech route obviously very desirable, so that militarising early may no longer be the default option. I haven't encountered later-game changes yet. Drama and Poetry being needed to develop Theology makes that route a big investment, and beelining it at the expense of other techs was a bad move in my first game (intuitively, getting Theology ASAP should maximise the Maya bonus - however you don't necessarily want to start churning out GPs that early in the game - Atlatlist and Pyramid give the Maya a pretty huge early game boost, so that they can wait a bit for the GP bonuses; how early are you going to want your only Long Count engineer? Admiral?).
Haven't looked at the changes to Wonders in much detail yet, but Terracotta Army seems a little underwhelming - essentially it replaces the old Stonehenge effect, but comes out later and gives only 6 culture rather than 8 (and an artist rather than an engineer). In my new game I'm stuck in a desert so I'll try getting Petra.
GPs: Not much to note, except that the Great Scientist now gives a research point bonus, as it did in Civ IV, rather than a free tech by default, which is a good improvement.
Policies: Only noting the change in Liberty's free settler, which makes the tree less of an auto-pick.
Religion: Saving the best till last. This is obviously the feature that has most obviously changed the early game. I don't like the limitation on number of religions - it was a weak point of the Civ IV religion system, and religion seems likely to be even more dominant in Civ V. Playing on Emperor I feel that, since they have gone down the restricted religion route, it should probably be harder for the player to be among those founding a religion; I've had no difficulty doing so in either game so far (although, granted, this is playing as a civ that has a strong early faith bonus). Either way, decoupling religion per se from the tech tree is good - plainly there's a relationship since investing in religious tech increases faith, but you're no longer constrained to follow a religious tech path to get early religion, and you may well have the option of allying yourself with a religious city state while you militarise or focus on the Education etc. tech path.
I was leery of the way religion was to be introduced, as it looked gimmicky and mechanical, there more to placate Civ IV fans than to enhance gameplay, but now playing the system I like it a lot. The faith resource works well, and the way different religious choices are structured - Pantheon beliefs being conceptually animistic and to a large extent based on terrain features and small, mainly early-game benefits, and later empire-wide and city-specific bonuses - is interesting. You can even essentially recreate a Civ IV religion - which resembles a Civ V religion with the belief that gives +1 happiness for every city following the religion and the one that gives a happiness bonus from temples.
Religion seems to spread very slowly, at least without trade routes - Tikal was close to my holy city of Palenque, but I still had to spread religion with a missionary. Tengrism only naturally spread to Uxmal, founded after I'd started the religion, with Palenque as the closest city, and with a trade route established soon after the city was founded (I'd chosen Messenger of the Gods as my Pantheon belief - not a good choice when I'd beelined Theology since it then took a while to develop the wheel...). I haven't yet reached a point where it spreads to foreign cities, and so haven't seen the diplomatic effects of religion in action.
Overall I'm impressed with the changes I've seen so far, including the ones I was wary of to begin with.
Moderator Action: Merged into the general "first impressions" thread.