Everything by Rare (except Mickey Speedway)..

World Driver Championship - best pure racer on the N64 by miles.

Resident Evil 2 - if you've not played it elsewhere already.

Star Wars Episode 1 PodRacer - Another damn good racer.

Star Wars: Rogue Squadron and/or Star Wars Battle for Naboo.

Forsaken - This game can mess with your internal balance.

Fighters Destiny - Very unique take on the fighting game genre. And a cow that will kick your ass. Gotta love it.

Body Harvest - Before Rockstar made GTA III, they made this.

Mystical Ninja Starring Goemon.

And anything by Nintendo is usually a safe bet.

Why not suggest Revenge since it was the sequel?  The games were fun but I never had the instructions so I never knew how to dodge while getting up.  Let me just say a friend took advantage of this and it eventually led to one of my last controller throws.  I never played with him again since the cheap bastard wouldn't tell me how to do it (nor did I care to look it up/figure it out).

Super Smash Bros.
Mario Tennis
Mario Golf
Mario Party 3
Worms Armageddon
Jet Force Gemini
Conker's Bad Fur Day
Perfect Dark
GoldenEye 007
Mario Kart 64
Paper Mario
F-Zero X

I can't believe nobody have mentioned F-Zero X.

Then if you liked the music you should check the Guitar Arranged version. Some of the best videogame-related music ever made.

Edit - Ninja'd by SethNintendo.

World Driver Championship! I'm so glad someone else loves that game.

And Fighters Destiny, too. An overlooked and underappreciated fighting game, for sure.

We only actually hit true 64 bit gen this gen. But have fun with n64. Jet Force Jemini FTW!

Oh my god, this.

I cannot stand Conker's Bad Fur Day. But Jet Force Gemini is a game worth looking into. As well, if you like FPS games, Forsaken is quite a bit underrated. Hybrid Heaven is a game that is just awesome. Even the cover art is sick.

There are many games worth the recommendation and people have listed so many. Knife Edge is one that gets overlooked but if you have friends, it is so much fun.

Diddy Kong Racing should be mentioned more. Far more balance than Mario Kart, more fun, better level design, hovercraft and planes. Grab that one if you can find it.

Banjo-Kazooie/Tooie, and Paper Mario if you haven't played (or played and liked) the GC version.

Get both Banjo-Kazooie games, they're glorious!
Also, Paper Mario, it's fantastic, and LONG!