What are, according to you, the games with the best AI. By AI, I mean "beats you on equal footing without cheating, or without cheating much".. I am not speaking of action games, where each individual opponent is often much weaker than you and thus you are supposed to wipe them.
Those great AI are rare.
For non-action games, I see two games with really outstanding AI :
- Rise of Prussia, the AGEOD simulation. It is the best AI I know so far. The AI will bet you if you take Prussia AND it may bet you if you take Austria & allies. Other AGEOD games have fairly good AI, but don't compete with the one of RoP.
- XCOM2 had a really good AI. UFO Defense was good enough, but in Terror From the Deep the enemies are not only cunning with their recon and approach, they also know how to use explosive weapons.(expect to see a lot of grenades land on your foot).
- Battle for Wesnoth has a very competent AI on the offense and on a "normal" map, much better than other games.AI.
- The freeware indy (rogue like) Smart Kobolds has... well... VERY cunning kobolds. They are only 40 of them, they are 100 times weaker than you, and they WILL kill you the first 2 times (at least) you play.
Most other strat' games I know have abysmal AI : Battle Isle (uh), Fantasy General / Elven Legacy, Panzer General. The IA of JA and JA2 was poor but not terrible.
EU3 AI and HoI3 AI were decent. Given the complexity of HoI3, the efficiency of the HoI3 AI is a feat.
Basicallly, most AI don't think strategically, moving their forces from one front to another or setting priorities between fronts, don't know when to retreat and save what can be saved, don't know how to scout, don't know when to attack and when to skirmish, ... Again, RoP is an exception. To give an example, I remember when I was heading toward Bohemia with a very strong Prussian force - the AI did not let me have one battle since it retreated all its armies and called back troops from minors front, and when I started to siege Praag, Austria moved around my troops and cut my supply lines. Then, they just waited for my unsupported siege to fail and my troops to go home weary and without supplies. Oh... did I mention that a huge army was waiting fortified on the way back, at the only spot where I HAD to pass (a gorge in Saxony) ? Well... as you can understand I love that game.
Any other great AI around ?

Starcraft and Warcraft series would get my vote. I think that it's not so much the cunning of the AI though, so much as the fact it can click everywhere at one. Whereas us mortals have to frantically navigate the map to keep everything in check.

Darkwind's AI is pretty crazy. They can learn from their mistakes i.e. self-adaptive. If the AI keeps getting slaughtered on a particular map, they will learn to change their routes and tactics. For example, they have learnt that, on some maps, charging head on gets them killed more easily. I've had the AI attempt to flank me before, while they sent a few of their guys to try and distract me. Then there's another incident where I was waiting for them at the top of the mountain, and they sent their entire main force on a head-on rush; while I was defending against this onslaught, two cars flanked me and shot me off the cliff. Crazy stuff.

AI War Fleet Command

operation flash point and arma series.

Condemned. The game FEAR tried to be. Condemned succeeded by scrapping scripted sequences and replacing them with cunning AI that will use its own initiative to get the jump on you. The odd thing is that the lessons learned here were never carried over to FEAR 2.

F.E.A.R. has a great AI.

+111
Condemned is my favorite survival horror of the past decade.

Half-Life 2 had excellent AI (although the level design limited greatly their effectiveness).

Get Penumbra! Nao!
HL2 is scripted. Almost everything is scripted, so the AI although good, is not that good. :)

I have Penumbra. Great game. Not as good.

Chess?:D
Well, i'd say Blizzard was never strong on AI. For example, one of the most basic ideas is path finding, and what units should do when the road is blocked. Path finding was bad in Warcraft 2, and still is today in SC2. Units making a big trip over the whole map, because they didn't wait 2 seconds for the path to clear. Units that find that the route they wanted to take is currently impassable, so they just stop. Units that twitch in one place, because they can't find the next step. ;)

I'm curious as to you suggested solution to that. Are you implying that the AI should be aware that some things are going to move? I accept that if you are funneling 20 troops through a tunnel, they should all go though, rather than walk around - and they do. Beyond that would require the AI to either predict what would happen, or respond to events after the path has been decided, which can lead to easy AI wacking where you just keep opening an closing a door to split the troops.
However I was going for the more macro AI, as an opponent it's hard, and plays by the rules. As an interface I've not personally been frustrated by it because I never move that many units.

In SC maybe, but in SC2 I've never seen any path-finding issues.

It was a little too rough around the edges to have the atmosphere it needed. They had all the right ideas, just not quite the right budget. Luckily Amnesia clearly addresses the atmosphere problem aplenty.
It was impressive when it was released, but Condemned trumped it on that front.