While I'm a bit biased to MMORPGs and story based RPGs (I'm not a fan of the mainstream FPS and fighting games, though there are a couple exceptions). Here's my honest top 10:
10) Battlfield 4 - only game in the series I own, I like it for the ability to think tactically rather than taking a "shoot anything that moves" mentality. However, it's so mainstream that you still get raging CoD addicts on there, which greatly detracts from the experience.
9) PokeMMO - I haven't even beaten the Elite 4, however a social kanto experience is a very fun twist on the games. It's not higher on the list because of the slow progression compared to the real games (that's how I feel, at least), and the disconnected social experience you feel from the very start.
8) Garry's Mod - I'm a sucker for sandbox games and even more so with one that contains both voice chat AND those reddit/4chan kids, making the multiplayer an entertaining experience to add to the already fun customizable single player experience. The only thing detracting from it is the buggy multiplayer and long load times of addons for servers.
7) Graal Online - Just all of the games, I don't know (and From what I collect not many others) what keeps me coming back, but I think it's because of the engaging community that makes you think of it as a social circle rather than a game. I think you all know its downsides.
6) Vindictus - With its great combos, badass weapons, and interestingly deep experience, I still play this with several friends both IRL and from other games. However, the combat makes it suffer just a bit.
5) SWTOR - I've loved Star Wars since I was a kid, and this game made me feel like I was living star wars. The full-voice overs and kinda- active combat make it engaging, but not addicting. The P2W elements and some complex elements to it make it a bit of a drag to play.
4) Pokemon - even with all the spin-offs it still holds it's own as a unique monster catching RPG with popularity and meta game experience that any gamer can learn to love. However, with the time it's been around, you start getting people with OP teams that make unique strategies and fun teams seem useless and disappointing to run.
3) Elder Scrolls Franchise - With lore that rivals even the real world and RPG Elements that bring casuals into the fun, the ES franchise never ceases to amaze with its newer games, even if it's a bland MMO that let down some fans.
2) Scribblenauts Series - Kinda like a sandbox mixed with a word game, Scribblenauts lets you use your "expanded vocabulary" shine by allowing you to just type a word in and make it appear in the world. You can create machines and screw around with a pink Cthulhu in a tutu if you want, the possibilities are vast, especially in the newer games.
1) Kingdom Hearts Series - I don't know why either but these games are so fun, and the story gets so emotional fans have gotten depressed off of it, Kingdom Hearts is a unique and fun RPG that will always ring the nostalgia bell in my head.