All of the Sonic games from Sonic 1 up to Sonic Heroes. By the time Sonic '06 came out I was in middle school and was starting a bit of a "everything I liked as a kid is stupid because I'm so mature" phase. Although the real reason why I didn't play Sonic '06 was because my parents refused to buy me an Xbox 360.
Also, a number of PS1 and GBA RPGs. On the PS1 end there were the ports of FF IV-VI and Chrono Trigger plus FFVII-IX not to mention other games like Threads of Fate or Star Ocean the Second Story. On GBA there was ports of FFI and II, Sword of Mana, Final Fantasy Tactics, the Fire Emblem games, Breath of Fire or, of course, the Pokemon series. Although I also played a decent amount of platformers on these consoles too like the original Spyro and Crash trilogies on PS1 and various S/NES ports on GBA like Mario 3, Mario World, DKC and Yoshi's Island.
GCN was also a pretty big part of my childhood. Both Metroid Primes, most of the Zelda games like Wind Waker, Twilight Princess and ports of Ocarina of Time and Majora's Mask. There was Tales of Symphonia, Kirby Air Ride, FF Crystal Chronicles, F-Zero GX and Smash Bros Melee.
Looking back, I played a lot of games as a kid. I don't even think that's half of the games I'd consider nostalgic.