An almost all Nintendo-published-titles library, like the selection available on the Wii / Wii U Virtual Consoles that Celine lists, is the most likely thing. We know Nintendo has the rights to those games because they are still available for sale digitally, and they are all good candidates for inclusion. I'm also going to assume that all of Rare's non-DK titles are, very sadly, out.
What I would really like to see, however, are Midway and Acclaim games, because they made a lot of fantastic games that are among my favorites on the system, and it's a real shame their N64 games haven't been re-released like most of Nintendo's do. The rights sshould be available, from Throwback (and Night Dive, for Turok anyway) for Acclaim and WB Games for Midway. For both companies, some of their better N64 releases are out because of age rating issues (the Turok games, Shadow Man, all of Midway's fighting games, Doom 64, Body Harvest...) or licensing rights issues (Midway's NFL Blitz, NBA Hangtime/Showtime, Wayne Gretzky, and such are sadly out, as would be all of Acclaim's sports games; their N64 baseball games, at least, are good.), and there's no way we'd see Wipeout 64 I am sure, but there are still some great ones that should be included.
San Francisco Rush 2049 - The most obvious one for me, Rush 2049 is the best racing game ever and I really love it. Nintendo will probably continue to ignore the N64's third-party library but they shouldn't. Include this amazing classic!
A few more Midway racing games it'd be cool to see include Cruis'n Exotica, Hydro Thunder, and San Francisco Rush. And for a few non-racing titles, Gauntlet Legends would be awesome if T-rated games are acceptable; that game is fantastic. There are also the Rampage games, though they're not great. It is frustrating how some of Midway's best games that aren't racing games are those sports games we wouldn't see because of rights issues though... too bad.
As for Acclaim, Extreme-G 1 or, better, 2 would be my top choice if the Turok games are out. Throwback recently re-released the PC version of XG2, so they have the rights. If T-rated games are okay, Forsaken 64 would be a cool one as well. (I also want to mention Iggy's 'Reckin Balls, it's interesting.)
... So not including M-rated games or things which have serious rights issues, what would I include in a ~20-something game N64 Mini? That's really hard, the N64 my favorite console and while it doesn't have the largest library, there are a lot more than 25 games on the thing I really like!
Definitely needs:
Super Mario 64
Ocarina of Time
Paper Mario
San Francisco Rush 2049
F-Zero X
Wave Race 64
Super Smash Bros.
Ogre Battle 64: Person of Lordly Caliber
Sin & Punishment: Successor to the Earth (the fully translated version we got on Wii VC)
Donkey Kong 64
Mario Kart 64
Star Fox 64
They should also include:
Goemon's Great Adventure
Mario Party 2 (or 3, though it'd probably be 2)
Kirby 64: The Crystal Shards
Pokemon Puzzle League
1080 Degrees Snowboarding
Excitebike 64
Bomberman 64
Castlevania: Legacy of Darkness
Tetrisphere (if Nintendo has the rights)
Majora's Mask
Extreme-G 2
Gauntlet Legends
Star Wars: Rogue Squadron
That's 25. Here would be my top options for inclusion not in the above two categories:
Star Wars: Battle for Naboo (the best N64 Star Wars game!)
San Francisco Rush: Extreme Racing
World Driver Championship (see below)
Top Gear Rally (see below)
Forsaken 64
Mystical Ninja Starring Goemon
Mario's Tennis
Rayman 2
Bomberman Hero
Cruis'n Exotica
Diddy Kong Racing
... And a title they likely will include but I never would put in the thing myself:
Pokemon Snap
For a bit more rights for on two of the games I mention above:
World Driver Championship - Midway published all of Boss Games' N64 games, including this popular sim racer, but Boss shut down a few years later so I don't know who has the rights to this one... does WB, or is it in limbo or something? It's not a favorite of mine personally, but it'd be a great one to include if they could.
Top Gear Rally (and/or Top Gear Overdrive) - Kemco published four Top Gear games on the N64. All of them are pretty good, but the first one, Rally, is the most popular so it'd probably be the best one to include. It is a pretty good game so it'd be awesome to see, if it could happen. (It's kind of too bad that none of the SNES Top Gear games were on the SNES Mini, though, so maybe it wouldn't happen... but it should.)
And finally... Nintendo would never put them in the Western version of the N64 Mini unless they secretly have translated copies lying around somewhere, but the N64 Custom Robo games are actually really good. They absolutely should put one in the Japanese version of the thing at least.
Beyond the games though, will the controller have a real controller pak port? I'd guess not? If they put any games with controller pak support in the thing and do support them though digital memory cards would be better, so that's not a big issue (unless it supported copying save files from original N64 memory cards, but while neat that isn't essential). What about rumble though, how will they deal with that? It really should have rumble... maybe build it in, yeah.
Rocket Robot on Wheels is a secret best game.
It is a great game, but if Sucker Punch owns any rights there's no way we'd ever see a re-release, sadly, since they're owned by Sony.