This is a great idea for a thread! I've got a few suggestions:
Kirby Blockball (GB) - A sequel would look awesome on 3DS in full color
Point Blank (PS1) - This whole series is amazing and one of the best light gun games ever. The series was never about fancy graphics, but it is a real shame that it is not on consoles or in arcades anymore.
Blast Corps (N64) - Its been a long time since I played it, but it was a lot of the fun back in the day and would definitely benefit from HD graphics.
Bully (PS2) - While the title is a bit passe now, this was a really fun and unique game. Definitely one of my favorite open-world games of all time.
The Bouncer (PS2) - It has its flaws, but I still thought it was a fun game and one that could have been improved in a sequel.
Okami (PS2) - This has been said but it definitely deserves one.
Final Fantasy Tactics (PS1) - While it got sequels, none of them compare to the original and the kiddie story and tone deviated way too far from the original.