Even though I already have an X-box and PS2, I am about to get a PSone/LCD screen combo mainly for travel. I am wondering what are some good games to get. I don't really like RPGs (although the only one I have played is FFX and I could not get into it). Thanks.

A few off the top of my head...

Gran Turismo I & II
Metal Gear Solid
Castlevania Symphony of the Night
Tekken 3
Street Fighter Alpha 3
Syphon Filter
Resident Evil 1, 2 &3

I can see why you don't like RPGs if FFX is the only one you've played. That game was pretty damn boring IMO. I suggest you give Grandia and Vagrant Story a try. Both have very different combat systems than the tired FF series.

I don't think there were many other PSX games I enjoyed. Driver was pretty good.

Wipeout XL
Ape Escape
Ace Combat series
Klonoa
Tomba 1 & 2
Raystorm
Raycrisis
Silhouette Mirage
Colony Wars

Tenchu and Tenchu 2

I agree with all these and would add the two Medal of Honor games. They were my favorite games on the system.

I agree with Jadakiss....Tenchu and Tenchu 2 are GREAT games
also
Medal of Honor (and if you like that, then Medal of Honor:Underground).
Grand Turismo (1)
and Resident Evil Series

I second some of these:

Ape Escape (needs to be more universally acknowledged as great)
Vagrant Story (yeah, kinda RPG, but SUPER COOL)
Colony Wars
Einhander
Syphon Filter

Gran Turismo
Tenchu
Tekken 3

I immediately thought of Tenchu when I read the thread title. Tenchu 2 didn't grab me as much, though... it's been a while since I played it, so I forget why. I think it was the poor controls.

I also really like the Metal Slug series... I'm pretty sure there's at least one Metal Slug game on the PS1.