A few that haven't been mentioned yet:

Silent Hill and Metal Gear Solid on PS1

If you're going to play any resident evil, I highly recommend 2 on PS1/N64/Dreamcast/GameCube, Code Veronica X on PS2/GameCube, The remake of RE1 on GameCube/Wii and 4 on GameCube/PS2/Wii.

If you're into more story/puzzle based games then you could also go for the Ace Attorney series, Ghost Trick, and Hotel Dusk all on the DS.

Legend of Dragoon (PS1)
Chrono Trigger (SNES)
First 2 Silent Hill games (PS1)

How far back do you wanna go? There is so many good NES games, but damn, they are a lot harder than I remembered. Thank god those controllers were so well made, when I was a kid I would toss them on the ground or wall when I was mad.

Wow guys thanks for all the great suggestions. It's amazing how many amazing old games are out there. I think I'm going to start with some of the Gamecube Zelda games that I've never played before. Up to this point I've only played A Link to the Past and Ocarina of Time. I am excite.

I really have no genre or era preference. I like a wide variety of games. Thanks so much guys.

the GC zelda games aren't as good as LttP and the N64 games

start with the SNES suggestions pretty much all of them listed in this thread are the bomb dot com

SH 2 is on the PS2 doggie. SH3 is also a PS2 classic and should be checked out, but only after you've played SH1. I haven't played SH4 but from what I've heard it's kind of hit or miss. Ignore everything after SH4. It's all stuff made by different developers that don't actually get what Silent Hill is supposed to be about and are all garbage. Also, don't get the SH HD collection. Konami completely dropped the ball on it.

Oh yeah, also go play Snowboard Kids 2 on the N64. That game is the fucking best.

Don't forget about MAME!!! Download that and go nuts on some classic 80's/90's beat em ups: TMNT, Simpsoms, XMEN, Double Dragon, Alien vs. Predator, Crime Fighters...etc etc

I also have the m2 Sega Arcade emulator with all the games - apparently these are even a bit difficult to find now. Hit me up if you want them.

what emulator are you guys using? been vaguely looking for a good one.

The ones I usually use that all work well and are pretty easy to set up are:
ZSNES for SNES, VBA for GBA, ePSXe for ps1. And while I don't really like playing 64 games on emulators, I'm pretty sure Project64 is still the go to emulator for that. No$gba and desmume are also both good DS emulators. I think I would recommend desmume over no$gba though. But I haven't used either of them recently. I generally prefer playing on the actual system and game since I own the majority of them so I don't really know if there are better emulators out there now. But those are ones that have always worked for me.

FF7
The Legend of Dragoon
Strider 2

All PS1

CTR <3 <3 <3

Starfox 64 is what I just downloaded.
But try to play melee online lol wonder how it'll feel with a 360 controller
http://www.smashboards.com/threads/dolphin-online-melee-netplay.335432/