I take it back. I do know of a game that uses UDP, as I totally spaced and noticed as I was playing it.
Darkages uses UDP, and it's fairly noticable in certain things.
Firstly, when you're moving, you can walk into walls and people, however once the packet telling the game you can't do that arrives shortly after, it "bumps" you back. However this often causes a problem we call "Screen shift", where the client now believes you're in a different spot than you are, and you end up being hit by monsters you think are off a few spaces, as well as missing targets you think you're hitting, and since spellcasting is click based, you end up trying to cast on the air, all because of datagrams.