Hogs of War - it's something like Worms in 3D, but from all the way back in 1998. The PS1 game works fine, but the PC release was bugged with enemy AI not moving at all.

Team Buddies - really fun action game on the PS1, could shine with 4v4 multiplayer on the internet

Jazz Jackrabbit - Bigger resolution at least, with more of the level being visible at any time. Modern controller support would also be awesome.