HSV/Beetle Adventure Racing has a debug menu, but has to be accessed via GameShark. It's probably one of the most best debug menus on a N64 game though.
The Urbz: Sims in the city on Playstation 2 has a debug menu you can unlock by doing some modifications to the disc. You can also get gameshark/codebreaker codes too. Theres a video by Video Game Beta Book of a debug build running.
I'm surprised no one mentioned this yet but Smash Bros Melee had an incredible debug menu. Shadowrun for the SNES had one too that wasn't discovered until last year. Same with Sim City for the SNES and Super Metroid. All discovered recently.
The original Time Crisis on the PlayStation has one, but you'll need a good CRT and a GunCon to activate it, it requires you to make several pixel-perfect shots on the title screen.