Don't know if this is even possible to put in.. but a .gif recorder
Not to cut past everyone else's suggestions, but I would really like that so damn bad. Instead, I'm stuck using 1964, limiting the speed down to 10 FPS, and holding F12 to take animated consecutive screenshots, import the screenshots into Jasc Animation Shop, erasing the background, pixel by pixel, and saving it as an animated GIF.
That's what I did with my current avatar (Luigi with is Running+A move)...it took hours. I also made this Ness avatar (Down+B move) from Super Smash Bros., but there's too much crust, so I only use it as my avatar on forums websites with dark backgrounds.
The reason I use 1964 to take screenshots is because it does it better for animated screenshots. Sure, you can slow down Project64 for better screenshots for animation using some frame buffer emulation of some kind, but the screenshots won't have perfect animation in between them like in 1964.
If this were possible, I would really like it if someone would put in some sort of thing in Project64 where you select some sort of option and drag a rectangle around the part of the game you want to log a GIF animation for and press Esc to stop recording or something like that.