This is hard to choose for myself. I don't think I can decide on one, so I'll stick with two (three technically.)

First up is Portal. Both games. I love the creativity and style. The fact that you could make a game with one protagonist and antagonist is very intriguing to me, even more so when I think about how there is only dialogue written for one! I personally thing the second game is better than the first, which is rare for me. I love how you get to actually see GLaDOS as more of a person and Wheatley was an awesome companion. Cave Johnson was also a pleasant surprise. Overall, the Portal series (as small as it was) will always be one of my favorite playthroughs.

Secondly, I can't not mention The Last of Us. This is one of the most creative and well-written videogames I have ever played. I loved how the player is highly encouraged to do more than "spray 'n pray" through the story. The hunt for supplies and ammo was challenging and fun. The story itself was very emotional and the cast was fantastic. I don't recall a game with a better voice-over.

Honorable mentions: The Elder Scrolls V: Skyrim, Kingdom Hearts, Super Smash Bros.

Gta (mostly the vice city version), because it was a very diverse game. You could do anything (except enter buildings) and not get bored. Have the police chase you or go about shooting everything. The graphics wasn't that good and neither was the physics and i also hated the fact that the water to land ratio was like 3:1 but try getting into the water with anything other than SEAWAYS or a boat and presto, you're wasted but there was (and still is) something about it that make it so stupidly interesting and an awesome game.
Looking forward to watchdogs :)

This is probably a phase that'll pass soon, but I'm currently really enjoying Triple Town. It's a fairly simple match-3 style game where matching items creates better items rather than removing them, with game-play therefore involving a lot of planning how to best utilise the small amount of ever-diminishing free space. I enjoy it because it's challenging and provides a number of different game modes, but didn't cost much -- it's a free-to-play title, and I purchased "unlimited turns" for about a dollar and have spent a small amount (less than $10 all up) on in-app purchases -- and is easy to play without having to dedicate large chunks of my precious free time -- I can just play for a minute or two and then put it away and continue later, and my longest whole games have only been around 30 minutes.

When I was younger and had much more time and less important things to spend my money on I really loved the Halo series; whilst they didn't really do anything original I felt they did a great job of combining all of the elements presented, had pretty minimal annoyances, and had a pretty good atmosphere and storyline.

I enjoy it because it's challenging

If you're into challenging thinker games, you should get The Room. It's somewhat of an "escape game" I guess, but very well built for a mobile app. It's also not even about escaping a room. It's actually about working with strange boxes to get them open. They recently released a second game but it's not free like the first one.

Link's Awakening, because of the excellent overworld design and item balance, and because of the way the game gets you to interact with the island's inhabitants, giving the story depth through gameplay as opposed to pure narrative.

I don't play games anymore, I have far too much fun or getting enjoyment from programming but back when I was an addict there were a few games I loved.

Loved once but hated in the end

EVE Online - For the politics and large fights involved, sadly the game went from chaotic warfare and politics to hand holding, inactivity and generic trolling.

WoW - The music was enough to make me play, the Redo everything next patch' was enough to make me quit

Still love

Tales of Symphonia 1/2 - The storyline was mature enough and not as predictable as other Nintendo games, great gameplay, great everything.

Eternal Darkness - Original, great storyline, great characters and just fun to play. Why they never made a second game still amazes me

Any Rare game on the N64 - This doesn't need explaining ;)

I was a fan of Nintendo games but the enjoyment I had died with the Wii and after MMOs failed to amuse me I moved on to RL which has a much better storyline than any other game out and better politics

Dungeon Keeper 2

Very innovative RTS game for it's time, this game forces players to overcome unique challenges that are presented.

Also have to deal with creatures you do not directly control, who can also get mad and leave ( or worse - change to the enemy's side ) if you do not treat them "good" .

Critters also have a leveling system from training and real combat.

I love the old "Megaman" aka. "Rockman" games, the new ones all suck.

Best game ever for me.

My favorite game for a long time was Kill Fun Yeah, but unfortunately it has a very small player base and there is no offline mode, so after the hype died down it became basically unplayable. The graphics and sounds are all really nice, and the small community that it had was really nice. It really needs to get on steam.

Ah crap, I just tried to play it and it doesn't work on intel graphics....

Otherwise, I have been into Rust lately, really fun to play with friends.

I love RPG, so I mostly separate my favorite games into styles:

Turn based is Chrono Trigger, hands down the best game I have ever player.

Hack'n'Slash is Soma Bringer, great game, I thank whoever translated the rom.

Strategy is Shining Force, first RPG I ever played in a video game, really great series.

Action is Tales of Destiny II (eternia in japan), really great and fun game... I laughed my ass out in many of the short cut scenes... also, best looking undine ever!