Some recommendations:
-Astal - Gorgeous looking 2D platformer.
-Darius Gaiden - One of the greatest shoot-em ups ever made, IMO. So much fun.
-Galactic Attack - Another great shoot-em up (although not as good as Darius Gaiden).
-House of the Dead - Very fun on-rails light-gun game with a zombie theme. But also pretty expensive, unfortunately.
-Marvel Super-Heroes - Great Street Fighter style fighting game from Capcom with eye-popping 2D graphics, and with Marvel Comics characters.
-Resident Evil - If you don't already have this game on the PS1, then this is a must-have. See where the series started.
-Shinobi: Legions - Great 2D action-platformer with Mortal Kombat-esque graphics (digitized), and oh-so-awesome live-action ninja cutscenes.
-Street Fighter Alpha series - It's Street Fighter. If you like fighting games, then these are fantastic buys.
-Panzer Dragoon & PD: Zwei - Fantastic on-rails shooters that have beautiful environments and music.
-Sonic 3D Blast - The definitive version of this game. But most people either hate it or love it.
-Virtua Cop 1 & 2 - Very fun, Sega made, on-rails light-gun shooting games.