PS1 aged better than the N64 bye a miles stone, and unlike the N64 there are plenty of 2D games available who look much better than anything on SNES and cost much less

Castlevania chroniceles
Castlevania SotN
Yu Gi Oh Forbidden Memories
Klonoa
Alundra
In the Hunt
Sonic Wings Special
Raiden Project
R-Types
Capcom Collection
Z
Breath of Fire 3&4
Suikoden 1&2
Vandal Hearts 1&2
Master of Monsters
Elementar Gearbolt
Point Blank 1-3
Rapid Reload

great 3D games
MGS
Silent Hill
Dino Crisis
Dead or Alive
Deception 2
MR Domino
Clock Tower

Crash Bandicoot 3, Crash Team Racing and Crash Bash are games which aged very good imo. ^^

A little list from me, ps1 games who still look great :

-Valkyrie profile (!!!!!!! No one said this name ? How ??)
-Vandal hearts 1/2
-Legend of mana (!!!)
-Vagrant story
-FF tactics
-Crash team racing
-Parasite eve 2/Dino crisis 2
-FF8/9
-Xenogears/The legend of Dragoon
-Breath of fire 3, and Breath of fire 4 (still looking pretty, i like it)
-Red alert (and command and conquer)

And maybe 2/3 others i forgot.

Chrono Cross always

I'm not sure about Silent Hill, game plays like garbage. Konami, redeem yourself and do a remake!

Every Squaresoft game that came out on it pretty much: FF7-9, Xenogears, Chrono Cross, Vagrant Story, FF Tactics, Parasite Eve and maybe some others I'm forgetting.

Metal Gear Solid

Resident Evil 1, 2 and 3

Some of the games people have suggested are inferior versions that really wouldn't be worth playing.  Take for example, the entire marvel vs. series on PS1 was gimped.  The series main attraction was being able to tag, but due to the PS1's lacking ram, that entire feature was removed from all the games in the series that appeared on PS1.

 But:

Mega Man Legends 2.  For me, the best aged 3D graphics game on PS1.  My original PS1 copy was stolen, so I now play it on PS3, but it's still great... Apart from Mega Man's voice.

Resident evil 1, 2 and 3

Mega Man X4

I can't recommend x5, or x6, because X6 wasn't supposed to be made, and visually looks and plays terrible.  X6 also has extremely high difficulty-- not due to creativeness, but out of poor stage design layout and enemy placement.  Not actual difficulty of trial and error.  It's all just memory and random luck when it really pushes you.

X5 just doesn't have the same creative standard that X4 had.

Can't suggest Mega Man 8 because the superior version is on Sega Saturn with added features and more enemies.  

That's all I've got without booting up my consoles.

Chrono Cross

Resident Evil 1-3

Suikoden 1 and 2

Harvest Moon Back to Nature

Haven't played many PS1 games but these were some of my favorite