Played some Super Mario World earlier (the All-Stars version, fuck palette swap Luigi), fantastic game. Same with Super Mario Bros. 3, glad to see them already getting a shout. Granted I've enjoyed most games mentioned so far that I've also played. Banjo Koozie was awesome, and so was Toejam & Earl. Was really disappointed when I bought the second Toejam & Earl game on the Virtual Console, not sure what they were thinking when they made that sequel.
Also, since Melee and DKC2 were mentioned, I'll just throw out that I personally though Brawl and the first game are the best out of the series. Donkey Kong Country 3 is pretty good too but nowhere near the caliber of the first two; same with the original Smash game except that was the first in the series so it's no disappointment. Oh, and since it's similar, glad Majora's Mask got the nod over Ocarina of Time, both are great but I always liked Majora's Mask better.
Finally, before I begin listing games, I have to say it's quite a shame I've just started a bunch of them recently and thus don't feel right recommending them. Both Chrono Trigger & Earthbound both could very well wind up as two of my all-time favorites (Chrono Trigger seems more likely at this point). Either way, I'll just go ahead and start my list of favorite games . . .
Super Mario RPG: Legend of the Seven Stars
Sonic the Hedgehog 3 & Knuckles (technically requires two games to get to work but were meant be the same game and most Sonic collection games include Sonic 3 & Knuckles as a game, however if it's not going to count because of that, I'll go with Sonic the Hedgehog 2 [which I like better but is "objectively" inferior])
Mario Kart 64
Tony Hawk's Pro Skater 3
Soul Calibur III
Star Wars: Battlefront II
Heavy Rain
Disgaea 4: A Promise Unforgotten
Xenosaga Episode I: Der Wille zur Macht
Smackdown Vs. Raw 2006
Dragon Ball Z: Budokai 3
Left off quite a few because I was trying to be more objective than just pure subjective even though that didn't stop me for putting some on most people probably wouldn't agree be on there. But for example, I love WWE Day of Reckoning 2, it's my favorite wrestling game ever with the original as a very close second. However, outside of having a somewhat interesting story (2 game only), it doesn't have much to offer outside of it's gameplay (which is incredible). Enough for me, but objectively a game needs more. Smackdown vs. Raw 2006 is a better choice, as it's probably the best wrestling game. Commentary that doesn't repeat during a match, fun/great gameplay with actually some difficulty and two counts (WWE '13), plenty of different match types (though DoR2 does have a fatal four way Last Man Standing match which is fun as hell), plenty of different game modes, etc. So stuff like that.