I really REALLY liked Little King's Story and Zack and Wiki

Astro Boy: Omega Factor
for the GBA

Box Boy (all of them)
for the 3DS

Exhumed (Powerslave) on PS1 / Saturn / PC (although the latter version is quite different from the console versions I hear). Fantastic Egyptian themed Doom clone.

Mischief Makers for the N64 probably, love that game, very bizarre and unique 2D platformer

Super Mario RPG: Legend of the seven stars. Sure, it had some success and critical acclaim but it was vastly overlooked as Super Mario 64 came out in the same year (I believe)

There should be multiple sequels for it. It should be a national treasure.

The Emperor's New Groove on PS1, I wouldn't call Disney games that underrated, but I don't hear much about that one.

Road Rash on the PSX

Terracon (PS1). Incredible platformer/shooter about an alien whose species were wiped out by a terraforming device and he has to stop it before it destroyed the universe. Featured massive open levels that I felt were a technical marvel at the time; featured a heartbreaking story and beautiful music and just generally brilliant for the platform it released on.

Gregory Horror Show (PS2). Quirky survival-horror comedy about capturing the souls of residents in a hotel to give to death in order to escape the hotel. Just absolutely bonkers yet so fun - all about placing traps so you capture the souls while escaping from enemies you've already beaten who want their souls back. Brilliant.

The Wonderful 101.,