I've never had much luck trying to play PS1 games on an HDTV. I tried playing them via a PS1 over composite and s-video... awful. Then I tried the PS2 over component and turned on smoothing or whatever in the PS2... still bleh on some games. Finally I ran composite from the PS2 and tried some different modes on the TV and finally got it to look playable. The game in question was FF7, for some reason the background textures (during battles and whatever) just looked horrendous and had lines etc in it. So annoying 
Well I haven't tried playing anything on the PS1 that's as graphically detailed as FFVII, but I have Legend of Dragoon on the way which is probably close. Parappa, Spyro and Jumping Flash 2 look pretty good on the HDTV, but I don't think those games attempt to be as graphically impressive as the FF games. They have simpler textures and lower polycount models, imo.
Nice! I played a little Sonic Pocket this morning (...and I still suck at it. Level 7 is where I'm currently stuck). And I played a little Metal Slug on the NGPC last night. I don't know how far into that one I am, but it's probably not very far. Last night I made it past the section where your plane is shot out of the air and you have to skydive/parachute without being shot. It took a lot of continues to get past that spot!
Are you talking about the water stage? I died a few times there but the airbase stage after that is a pain. Which game would you recommend Dark Arms or Metal Slug?
Yeah, I'm not really too sure where I was in the game.

I hadn't played it in ages (probably years) and turned it on on a whim and pressed continue. My character had to skydive, timing a button press to open his parachute before plummeting to the ground, and at the same time moving all over the screen to avoid being shot down by some unseen gunfire. Once I made it past that level, I moved on to an area that had a lot of elevators and doors that lead to other sections of the level. Lots of tanks and baddies. I find it really hard to play that game on the NGPC, because I have to hold the console "just right". If I move it around too much while playing either I get a ton of glare for the lights in the room, or I can't see what's going on due to the relative small viewing angle. And I never got good with the little joypad. I find it's way to easy to press a diagonal direction when I really just want to move left or right. I have Pac Man for the NGPC and it's frustrating.