I do think it's a bit odd how you're doing this to find out what's considered a "great" game but asking for everyone's favorite games. I'd consider the games that are my favorite to be better then a simple "great." Anyway, I'll contribute.
Shining Force 2 Super Smash Brothers Melee Starcraft 1
Not necessarily my top 3 favorite, but they're up there. Just trying to add some more flavor.
I didn't list literally my 3 favorites, but games that I always come back to. My favorite games change regularly and honestly trying to use my absolute favorites in history would skew this even further towards super high rated stuff. The games I keep coming back to, though? Those are truly great games, I feel. --- If you think my name is silly, you should call me either Rob or LaughingThesaurus. No need for being strictly formal on a message board, right?