Not sure if I'll come up with 10, and these won't be in the exact order I want them most likely... well, let's try.
1. Baldur's Gate Series
2. Ragnarok Online
3. Final Fantasy Series (Especially X and XII - see below)
4. Neverwiner Nights (Not the actual game, the online modules that I've played - Aeranor and a few others)
5. Guild Wars
6. Phantasy Star Online Ver2 (Dreamcast)
7. Super Smash Brothers (Mostly Melee, but I've enjoyed all of them)
8. Bubble Bobble
9. Pokemon Red/Blue (never played any of the others)
10. Spider Solitaire
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Breakdown
1. I've spent a lot of time on these games. I loved the original when I was younger. I still enjoy playing BGII + ToB expansion, just because of how stupidly powerful you can become.
2. I wouldn't waste so much time on the game if I didn't love it. Incidentally, I wouldn't be posting on these forums if I didn't either.... so yea.
3. Okay, there are specific reasons I like X and XII best, and it's because they're the only ones I've spent time to make stupidly broken characters in. Example: In Final Fantasy X, I decided (when I was bored one summer during college) to re-engineer the sphere grid so all my characters would have 255 in all stats and around 64k-ish HP (I think, can't remember). I haven't actually finished yet, the grid is still missing some HP spheres and Luck spheres...it's silly fun to watch Lulu deal 99999 damage with a doll. Example 2: I currently have a level 70-something Vaan in FFXII, and I haven't even had whats-her-face join my team yet... I just enjoy doing silly things with these games.
4. Some of the modules made for Neverwinter Nights were amazing. Some guy who went by Igulfast made a server called Aeranor and it was amazing. I spent a lot of time playing there, even though the player base was like 30 people. Yummy fun.
5. Guild Wars. I have a love/hate relationship with this game. I don't actually think the game itself belongs on the +10 1337 Games list...but I'm still addicted to maxing titles in this game, even though I'm no longer entertained by the game itself. If you offer me an objective version of "perfection" in a game, it's enough to keep me hooked. They also made me hate them by making two of the titles mutually exclusive, so no matter what I do I'll never have EVERY title on just one character.
6. I had actually forgotten about this game until a few days ago (ironically), when Herman was playing it in his room. Since then I moved my Dreamcast from my parents' house to my apartment. I haven't played more than an hour so far...but I'm sure a lot more time will be wasted leveling one of my characters sometime soon...
7. Fun with friends, fun online, fun fun fun.
8. If anyone says this game isn't amazing, I'll cut you. Simple as that. this game is FULL UP on WIN.
9. Whatever. I enjoyed them when I was young. I still sometimes pick up my game boy when I visit home (I gave it to my little brother) and mess around with it.
10. I couldn't think of a "legit" 10th game, and I play this one when I'm really bored. There you have it.