I don't know about which is the worst of the PS1 games. Here are the games I would like to see on the service:
Resident Evil 2
Resident Evil 3: Nemesis
Metal Gear Solid
Final Fantasy VIII
Final Fantasy IX
Final Fantasy Tatctics
Gran Turismo
Gran Turismo 2
Wipeout 2097
Wipeout 3
Tomb Raider
Tomb Raider II
Suikodein 2
Chrono Cross
Those are the ones I'm really hope we see on PSN, I could name many others but these are the one I look foward to the most.

Currently I'm hoping for the MegaMan Legends games. I've personally never played them, but a friend of mine praises them to high heavens. I hope he's not just being nostalgic.

I also remember a shooting game that I once played on a demo disc. I can't for the life of me remember it's name, but I remember it was 2.5D, the level took place in some kind of futuristic city, and the boss at the end of the level would change it's shape to attack. I bet that narrows it down to at least 10 games, huh?

It's so weird. When the Legends games first came out, everyone talked about how awful they were. Now I hear people speaking highly of them pretty often. I can't remember if I actually played them. They certainly looked bad, even at the time.

@Adam: they did look really simple compared to other PSX games (or at least the first one did; i remember i was not interested in playing MML at all, but my then-boyfriend said it was a good game, so i gave it a shot), but i really had a lot of fun playing them.

Would this be that game Buster? Contra Adventure
http://www.romulation.net/files/screenshots/roms/PSX/24412/s_...

No, that's not it. In the game I'm thinking of, you controlled a flying ship.

EDIT: I talked to a friend of mine, and he remembered the game. It was called Einhander, or something close to that.

1. Vagrant Story
2. Einhander
3. Gran Turismo
4. Mega Man Legends (both)
5. Legend of Legai
6. Brave Fencer Mushashi
7. Oddworld (all)
8. Heart of Darkness
9. Final Fantasy 9
10. Crash Team Racing

Thats my top ten.

I loved the Twisted Metal games and Spyro games on the PSX.
Oh and MGS is probably my favorite game on the system

Well slapshot, supermarioman, and castlehominid basically covered the majority of the ps1 loot.
Couple I didnt see:

Legend of Dragoon
Legacy of Kain: Blood Omen

Fear

No particular order:

1. Xenogears (the disk I had malfunctioned when I was early in the game, so I definitely want it back!)
2. Crash Bash (for the memories. Still have it too)
3. Vagrant Story
4. Final Fantasy VIII
5. Tomba! 1 & 2
6. Suikoden II
7. Einhander
8. Ehrgeiz
9. Paraste Eve 1 & 2
10. Vib-Ribbon (c'mon Sony, make with the imports!)

Also: All the Twisted Metals, the old Wipeouts, Soul Blade, Crash Team Racing (really wanted this one as a kid, but never got it), Alundra 1 & 2, the Raiden Project

Games I hope will NEVER appear on the service:

Q*Bert
Driver

On PS1 there's one game I always recommend. The only reason I don't still play it is because I don't have a PS1 anymore. If it was rereleased as an emulated title I'd snap it up immediately.

Exhumed .. it's an FPS set in Egypt. Amazing graphics and a fluid, natural control scheme. Good selection of weapons including some based on mystical anciend Egyptian artefacts. This game is the nutts.

Video - http://www.youtube.com/watch?v=LjQ-DcycgzQ

Incidentally, this game was called Powerslave in the US.

I'll just add 2 RPGs that aren't already on here:

Shadow Madness
Guardian's Crusade

And 2 Action games:
The Misadventures Of Tron Bonne
Tail Concerto

Crash Bandicoot Warped. 'Nuff said.

Only one said Tomba!/Tombi!

That's a great PSX game. Y conmpleted it nearly ten times, and never got bored of it.

Also, Loaded, it was also in the Saturn.

Aside from Suikoden II and Megaman Legends, I'd like to see Threads of Fate hit the PSN. It was a fun little adventure RPG.

I forgot about some games!!!!!
Dragon Quest VII
Klonoa
Klonoa 2
I can't belive I forgot these and that nobody else has mentioned them!!!

Mobile Light Force just came out! I've never played it, so I'm pretty excited despite the fact that the localizers completely removed the story, which was surely hilarious if Castle of Shikigami III is any indicator. It's a shoot them up game by the makers of Shikigami III (great Wii game) and only $6.

Sorry Wii Music, but it looks like I will have to cancel our evening plans.