Seems all my favourite non cRPGs have been mentioned already...
Well, here goes(in no particural order)
1) Prince of Persia: Sands of Time
I like this game because it's the first game I actually knew how to play, well I did die a lot before actually learning. I also like the story of the game, mostly because it reminds me of the Thousand and one nights type of stories. I have a soft spot for the Disney animation Aladdin so that maybe explains why I love eastern fairy tales.
2) Warcraft III
I quess I like this game mostly because of the character of Arthas, I especially liked the clip where he kills his father. Another reason for liking this game might be that it was the first Blizzard game I owned and played through, maybe a bit like finding some type of cuisine you really like as in "I really like this company's games".
3) Rome Total War
What's best about this game is making enemies rout. In TW it's a battle of keeping your men more motivated, while in most RTSs it's a fight to the bitter end. Maybe I also like the game because you get to play as Romans, which would explain why I don't like Medieval 2 TW so much.
4) The Longest Journey(not Dreamfall)
Again, I liked the character of April so much I just had to find out what happened to her and ended up completing the game rather fast. The nutty humour is also wonderful, would like to play the game again just to play hopscots with the sorceror, the one who stole the wind, again. I haven't played any of the classic adventure games so could be like drinking something I'd never tasted before and noticing it tastes great.
Damn, can't think of a fifth game I really loved... I quess I'll make it a top four list.
nah, got one more (which hasn't been mentioned yet I think):
5) Escape from Butcher Bay
If Prince of Persia was the first platformer I learned to how to play without sucking at it, then Escape from Butcher Bay is the first FPS I didn't suck at. Before I played this game I wondered why some people thought Vin Diesel was cool, but after playing it I pretty much found out. I also liked the melee fighting system and the characters you could talk to(not so typical for a FPS).