I found Resident Evil 2 on the N64 to be better than the PS1 version, especially when using the RAM pack, however, the audio was quite compressed due to the cartridge, capacity limitations, so it sounds quite muffled in comparison to the PS1 version.
Tony Hawk's Pro Skater 1 & 2 are essential if you're into skateboarding games.
Banjo Kazooie still holds up today as it's a brilliant platformer. Also, Gruntilda's terrible, terrible jokes.
Bomberman 64 & Bomberman Hero, maybe I just view these games with nostalgia goggles, but they're two of my favourite N64 games. The boss battles, the incredible soundtracks, etc. These are definitely worth playing.
Doom 64, it's Doom on the Nintendo 64, what more could you want? Also, the soundtrack is fantastic, one of the "creepiest" games you'll ever play, if only because of the soundtrack.
Duke Nukem Zero Hour, what? I enjoyed it. 3rd person Duke is fun!
Jet Force Gemini, arguably one of the best releases for the N64. Quite fun.
I'm probably viewing the majority of these with nostalgia goggles, but that doesn't matter, these are all games I definitely recommend. Also, please excuse the grammar, I'm quite sick and it just doesn't seem as important as it usually is to me.