Mine would be based mainly on how I felt at the time - which had the most impact
1) Final Fantasy X - amazing characters, great story and awesome gameplay. So immersive. The perfect game
2) Super Mario Bros - the original and the best - I was obsessed with this
3) Mortal Kombat 2 - so much fun and much more polished than MK1. Got me hooked on the series (mainly thanks to Kitana/Mileena/Raiden!)
4) Street Fighter 2 Champion Edition - Hands down the most important fighting game in history - and worth the title
5) World of Warcraft - so well done, you can sink full days in to it
6) Mortal Kombat 9 - best "best of" game ever
7) Everquest - The best thing about this game was how social it was. It was like a community - I have never played anything like it. There were few assholes on this game as if you got a bad reputation, you were screwed - it was a VERY tough, unforgiving game and very hard/slow to level solo. If you couldn't play well with other people, you may as well give up. There were lots of RL friends and relationships being made on here (my friend met her boyfriend who relocated to Melbourne from London on this!)
8) Civilization 3 - the whole Civilization series has to be the most addictive game out once you have started a map... JUST ONE MORE TURN!!!
9) Mortal Kombat Deception - the most underrated in the series. It set the stage for future games with conquest, chess mode (my favorite ever!) etc etc
10) Kid Icarus - one of the most underrated games of all time
Honorable mentions to Double Dragon, Mario Kart, Ocarina of Time, Final Fantasy 13, TMNT Arcade, Super Mario World and Uncharted 4, Mortal Kombat X