Oh man, tough question. Ask me on a different day and you'd get a different answer as I remembered some other game I used to play 'til my eyes bled. Still, I'll try. To amalgamate all the different criteria - fun, replayability, content, nostalgia value, etc. - I'll go with what Toellner did and judge them by effect on my life crossed with my objective evaluation of how masterful they are. I'll also need a different reason for every game I pick - so I won't just have ten games that I love for the same damn reason. Star Wars: Battlefront isn't there because Halo is, let's put it that way.

[hider=Top Ten]
10. Portal 1/2 - this is how to write a game. The dialogue is hilarious and GLaDOS is just an incredible character. The fame of the cake and the companion cube are testament to the excellence of the writers - these are not developed characters or plot points that we spent time getting connected to, but they entered pop culture nonetheless thanks to the excellent writing. It helps that they are excellent little puzzle games. The Portal games are "light" gaming done right.
9. Dishonored/Metro 2033 - seem an odd pairing, but I put them together because for me the thing they did best was //atmosphere//. They immersed me not through compelling characters or fascinating worlds (though I quite like the world of Dishonored, in particular), but simply through a mixture of soundtrack and graphics and whatever else that contributes to the tone of a game. The fact that I can't put my finger on it, that I can't even say what captivated me, says a lot for these games.
8. Minecraft. Compared to most people I barely played, but it opened up my mind a lot in terms of the incredible potential games can have, and I still remember the sense of absolute wonder that captured me standing on top of a hill and looking out over the world I could mold. It pushed the boundaries a bit, and that deserves admiration and commendation.
7. Deus Ex: Human Revolution - a mixture of excellent, diverse gameplay where you can choose your own style of play with a compelling story, a gritty, dark cyberpunk world that addresses complex themes on the moral and social level? God, please yes, give me more. Games like Splinter Cell of a similar ilk are also enjoyable, but DE:HR stands out because of its inclusion of deeper moral questions and thoughts. Sure, the game doesn't revolve around them, but it does mention them in a not-entirely hamfisted way, and that's a rarity enough in games.
6. Pokemon (particularly Ruby) - come on, how is this not on every single list?
5. Jak and Daxter series (particularly Jak II: Renegade and Jak: 3, with honorable mention to Jak X)/Ratchet and Clank series. Holy fuck, I played these series to death. Platform games at their absolute finest, with great and likable characters and immersive, intriguing worlds.
3B. Fallout/Elder Scrolls - open world gaming done at its best. Forces you to do nothing and entices you to do everything; it truly feels like your adventure. To me, that's an incredible achievement, and I have sunk stupidly large amounts of hours into them for that reason. Instead of spoon-feeding you anything, it makes things feel much more realistic by handing you a world and saying "now live in it". Fantastic. I always see these two series and Mass Effect in a similar way, as two sides of the same coin - ME is more streamlined, but achieved a similar immersion and sense of a living universe. Truly, this is //escapism//.
3A. Mass Effect series. Absolute genius, in my opinion. The prime example of how to make a game more than a game - to make it a story, an adventure, and interactive film that's still fun. Some of the tougher choices I had to make throughout the series legitimately stuck with me and had me deliberating for an hour.
2. Mirror's Edge. I've played this game through a ridiculous amount of times, and the second one coming out soonish has me in fits of excitement. An enormous amount of fun to play, and the prime example of how movement should work and flow in a game. Plus, it tackles interesting themes without cramming them down your throat, and the notes of rebellion running through the game still appeals to me as much as it appealed to my angsty metalhead teenage self.
1. The Halo games, obviously. My 13-year-old self even named my original RPG account after it, I spent so much time playing them with people. The social aspects of Custom Games, Forge, and Theatre turned what was already an amazing series, a series renowned for excellent mechanics and epic sci-fi storytelling, into the perfect shooter. I have memories I'll never forget and some of my oldest friends from playing this - the games were genuinely important to my life for a long while.[/hider]

[hider=Honourable Mentions for Nostalgia Reasons]
Ty the Tasmanian Tiger - purely for nostalgia, I love this game to bits. It was my first game on the PS2, on a console, and it was brilliant. It was so hard for me to play as a 5-year-old and me and my family bonded over trying to eventually beat it together, which took us years. The world and different levels felt huge and diverse at the time, and probably still would if I played it. It actually made me //want// to hunt down all the bloody collectibles. 
Star Wars: Battlefront - played this endlessly with my brother. Although I feel Halo has to rightfully take the place for most influential and best shooter on my list, and there isn't really space for another one, this game and its sequel were pretty incredible.
Spartan: Total Warrior - it was a very well-designed and enjoyable hack-and-slash that really challenged me when I was younger. Its setting in Ancient Greece and its inclusion of lots of Greek mythology made a big impression on me as a kid, and even today I have a massive interest in that mythology. I haven't played it in years, but god did I as a kid.
FIFA 2002. I feel the need to justify this one, so prepare for a spiel. I used to be a huge football nut when I was a kid and I killed hours on this game. FIFA gets a lot of hate and can't really be considered a masterpiece of gaming, but I do genuinely think that they're great games for social play. It is excellently balanced from a multiplayer sense, for starters, but it also rewards skill more than anything else - you don't automatically get better by playing for ages, unlike shooters where you unlock bigger and better guns for example. It reminds me almost of a "strategy game light", almost like a quick-paced mini-RTS. [/hider]