1: Legend of Zelda: Link's Awakening
2: Super Mario 64
3: Counter-Strike
4: Legend of Zelda: Ocarina of Time
5: Heroes of Might and Magic III
6: Baldur's Gate 2
7: World of Warcraft
8: Pokémon Red/Blue
9: Dragon Age: Origins
10: Super Smash Bros. Melee
Explanations:
Legend of Zelda: Link's Awakening
I think this was one of my first games, definitely my first Zelda game at least. I remember getting into this game, wanting to find all the secrets. It had probably the best gameplay of all the Zelda games, and also a charm which I can't find in any games today. It was hard then, and still is, but not too hard.
Super Mario 64
Still the best Mario game, no questions asked. The levels are almost perfect and IMO the graphics still hold up really well. The levels were just so memorable, and had some great characters. It has almost flawless controls, which is something that can't be said about any other Mario game. Many like to argue that Galaxy has great controls, but I've never really felt that. Mario doesn't feel like a ninja anymore!
Counter-Strike
Probably the best online game I've ever played, and definitely the best shooter. It just feels so great to play, blasing those headshots. It's a lot simpler in concept than most shooters today, but so much harder to master, and I think that mix of accessibility and depth worked in its favour when it was still fresh. Although, it has gotten really hard for new players to get into as everyone still playing this game have been for many years already.
Legend of Zelda: Ocarina of Time
This game is just magical. The overworld, the characters, the dungeons. In my opinion the best dungeons of any Zelda game, they're just so intricate. The water temple alone proves my point.
Heroes of Might and Magic III
I had so much fun playing this in multiplayer with my friends when I was younger, and I still do. It's hard to put my finger on what makes this game so damn fun, but I'd say it's the great graphics coupled with the weird basebuilding that the game actually has, and its RPG mechanics. It's pretty much an SRPG, though most people don't think of it as one.
Baldur's Gate 2
Great writing, great characters, great combat. I wasn't really much into traditional RPGs before playing this game, but it really turned me over. The AD&D rules weren't that hard to get on a basic level, however there's so much to know if you really want to dig into it. The game has an endless amount of sidequests, probably the most I've seen in an game, and if you want it to, it can keep you occupied for a veery long time.
World of Warcraft
Obligatory I feel, Blizzard created a masterpiece with this game. The art is just great, and they really managed to turn the Warcraft universe into something that can last for a long time. When I quit playing, my account had around a total of 80 days played. I'd guess that is about five times more than I've ever played any game, even games like Counter-Strike. It keeps you occupied, and it delivers.
Pokémon Red/Blue
When I was a kid I always carried a handheld with me, more specifically my Gameboy. Why? Because it had frickin' Pokémon! Any free moment I had, I was playing it. I've finished my Pokémon Red so many times that I've lost count, but I'd guess it's over 15 times by now. I've speedran it for the heck of it, and I've gotten 6 of my Pokémon to level 100. (some cheating involved, but not too much!) My best memory is probably when me and three friends spent three whole days playing through the game, aiming to catch all Pokémon.
We did this just a few years ago, and boy was it a nostalgia trip.
Dragon Age: Origins
Again, Bioware delivers. This kind of game had been missing from the gaming scene since Baldur's Gate 2 came out, and it really was its spiritual successor. The writing was really good, and the characters really came to life with great VA.
Super Smash Bros. Melee
I have never been into 'real' fighting games such as Mortal Kombat or Street Fighter, this is really the only one I can bare playing. and boy, do I like it. All my favourite characters are in this game, and the all control really well. I still play this game with my friends when they come over, and we have a blast with it.