A while ago I read the Notenki Memoirs which is a book about the founding of Studio Gainax (the creators of Evangelion). One of things it mentions is how back in 1981 and 1983 the Gainax group hosted a couple of anime conventions called Daicon 3 and Daicon 4. It also said that they created orignal anime videos for the openings of those conventions, and how impressed everyone was with them.
Well, I just recently found somewhere you are able to download the videos (or, if you prefer, the YouTube versions are here and here). They are great! Keep an eye out and see how many characters you recognize.
On another note, if you ever saw the 5th episode of FLCL you might remember Haruko flying in to a fight wearing a bunny outfit and shouting "Daicon 5!" You'll see where that scene came from if you watch the Daicon 4 video. (You can see the relevant scene in FLCL in this music video, about 45 seconds in.)
Another homage to Daicon 4 apparently can be found in the Gonzo-produced Densha Otoko opening animation. A comparison of the the two can be found on YouTube.