Bit of a weird question to ask lol, are you expecting a list of every compatible game? The easiest way to see if the game you want to play is supported is to just go onto the store page itself and check.
You should see something similar to the above on the page, and clicking "Learn more" will tell you why it's got the rating it has. It's also a pretty good indicator if a game will run on a lower spec PC, so I do really like it.
For games you already own, there should be a library filter to just show games that are verified or playable, so that would be a good starting point on that front.
I would recommend looking at https://steamdeckhq.com/. They post updates about supported games more or less often. From my experience would say that some games, which officially not yet declared as supported (e.g., Mortal Combat 11, as far as I remember) may work. However, you'll never know unless you try.
Protondb.com is also a good source. It crowdsourced the question since proton came into existence. Even now: when a game is marked unsupported, you'll usually find people using tweaks to get it to work as it should (eg stealth inc 2 required changing one shortcut to the game to make it 100% workable). Sometimes the info is flat out outdated (valve doesn't retest every game if they update proton), so your game might work without a hitch.
But while there are a few exceptions (rough estimate i'd say 5% of ALL games), pretty much anything that plays on windows works with the steam deck. Most notable exception is(iirc still) games with anti cheat drm like dumovo. I've heard of games that were playable as a cracked version because the official version had some stuff to - ironically - prevent piracy. Newer games seem fine (eg hi-fi rush), but i can't say I've got statistics.
Still: exceptions aside, the short answer would be: it plays everything.
(my main concern is usually the text size and control scheme: there's not much advantage to being able to play a game that's really meant for keyboard/mouse or has tiny text due to the screen size)
However while that list is updated as they test games it's only the games they have tested and verified to work well. More games than what they've been able to test will work, but you might have to give it a try yourself. Combined with protonDB and steamdeckHQ this is pretty much every list to check on whether something might work or not.
Dungeon Keeper
Starcraft
Starcraft II
Warcraft III
Ragnarok Battle offline
Settlers III
And also a few games from the Steam library.
Joke aside, so far everything runs, I never check the compatibility icon because I play unpopular trash games nobody bother trying on SD. Sometimes, just use a bit of proton magic, but you'll always get results.
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