Old school/retro gaming is some of my favorite. It's like jumping in a time machine every time I play them.
Anyway, most of my favorites are on the NES or Super NES.
NES - The SMB games, Castlevania games, Zelda games, Double Dragon games, Metroid; plus some of the more obscure titles like Strider and Code Name: Viper.
Super NES - Super Metroid and Zelda were my 2 favorite SNES games by far. Zelda on the SNES is still my favorite Zelda game after all these years.
I know it sounds weird but in many ways I still have problems labeling the N64 and PlayStation as "old school" even though both are over 15 years old now. I guess it's because I was close to 20 when they came out. I loved the PS, it had the Resident Evil games, Dino Crisis, Metal Gear Solid, Silent Hill. But the N64 was always disappointing to me. Sure I loved Super Mario 64, both Zelda games, GoldenEye and Perfect Dark but after that it just seemed like overall it didn't have all that many great games as opposed to past Nintendo systems.