Metroid Maybe?
At the Game Developers Conference on March 18, Shigeru Miyamoto revealed that Metroid was being developed by EAD (Nintendo's in-house development team). He also stated that while he's not directly involved with the project, he does stop by now and then to check on their progress. He did not, however, specify which machine the game will be released on. Could the new Metroid game find its way to N2000? Time will tell.

Retro Studios
Retro Studios will be a second party developer for Nintendo, much like Rare is now. They are almost assuredly working on a sports title (probably a football game) and rumor has it that they're also working on an online RPG to launch with N200X.
Read what we know about Retro Studios.

Left Field Productions
Left Field is another Nintendo second party and has been confirmed as a developer for the next generation Nintendo. They were responsible for Kobe Bryant in NBA Courtside on N64 so expect them to produce a basketball game for the new machine. Once again, Nintendo is showing its committment to sports games.

1080° 2?
A sequel to 1080° Snowboarding was supposed to come out on Nintendo 64, but the project was halted. It's possible that the sequel will be made for the new Nintendo machine.

A New Mario
When IGN64 asked Shigeru Miyamoto about the next Mario game, Nintendo's greastest video game designer had this to say:

"We have made the outline for Mario 2 more than one year ago, but I haven't touched it since then. Luigi and Mario are running on the display on my desk right now on the disc drive... Maybe I will ask some other people to work on it, or maybe we could think about making it for a completely different system -- but I don't know at this point in time."

OK, so that doesn't really mean much besides practically confirming that the sequel to Mario 64 will not be on Nintendo 64. However, the interview was conducted in early February (or some time around there) of 1999, meaning that as of that time nobody was working on the next Mario game. Hopefully, they will have started by now, as two years may not be enough time to finish a game (at least not at the level of quality Nintendo is known for). Launching without one of their major franchises would be a costly mistake.
Read the full Miyamoto interview here.

More information that has been revealed since then not only confirms that Mario will once again launch with Nintendo's new system, but that Luigi be featured in the game. Shigeru Miyamoto has also said he wants to make Mario more "grown-up", suggesting that the future Mario title won't be as cutesy as previous versions.

Unfortunately, that's all there is right now. Nintendo EAD (Entertainment Analysis and Development, Nintendo's best development team of which Miyamoto is the head) doesn't seem to be working on anything exciting for Nintendo 64, so one can safely assume that they've begun working on games for the new machine. They had better be. They have less than two years to try out the new hardware, design a new game, and then actually implement it. Knowing Nintendo, their games will be a sight to behold. Stay tuned for further developments.