This list is likely inaccurate in order, may be better described as listed by internal significance.
5. Spore Creature Creator
Someone got me this demo before I got Spore. While I did enjoy the actual game—and certainly did more creature creating in the full version—the part that makes it great to me basically boils down to this. I've always loved animals, and being able to design some myself was great—even if I mostly just made pigs, boar, and other various swine.
4. Warcraft III: The Frozen Throne
I liked the campaign, mostly for the story and characters. The melee gameplay was okay, I was never a big strategist. What really stuck with me were the custom games. SotDRP, Werewolf — Transylvania, and oooh, Elimination Tournament. Blood Tournament. The one where you built spells from elemental orbs. Just so much variety and so much fun. Even the map creation tool was amazing to play with.
3. Shadow of the Colossus
Just, yeah. Loved it.
2. Dragon Age: Origins
Just recently finished my third playthrough, so I've now played at least a hundred hours. Though I'm no biggie for RPGs, the ability to choose who my character was in a story significant way is what really drew me in. The gameplay also wasn't too bad. I'm sure there are other games that did the choicey storyline better, but this is the one I played, and many of the characters I encountered I simply adore.
1. Demon's Souls
I know, I know, Dark Souls is better known. I personally never got the chance to finish DkS, so this is the one listed. As of yet, I liked this one better because of the feel of the game, with the Nexus in particular being a location that I think back to nostalgically. In a way, DkS has always felt like an extension of DeS, so the original will probably stay my favourite, even if DkS is bigger and better, with a deeper story. What I really love about this game, of course, is the combat. I just like how it plays. (Aesthetically cool too.)
Uhhh, that's only five games. I have other games I love, but I guess nowhere near as much? So, honourable mentions:
Star Warfare: Alien Invasion
Tap Tap Revenge 4
Myst
the Walking Dead: Season 1
Uncharted series
Some Ratchet and Clank demo.
A variety of Lego Star Wars games.
And no, I've never played pokémon. Nor Mario. Unless you count Super Smash Bros: Brawl. But even then, I always played as Kirby. ;]