Executive Meddling: Why Mega Man 3 is one of Inafune's least favorites. He said that it could've been a much better game if the team was given more time to polish it, but Capcom wanted it released as soon as possible to capitalize on the momentum garnered from the second game, and he had to replace the head of production to complete it. However, the third game is still loved by most of the general public, though not as much as its predecessor.
Wily and Right's RockBoard: That's Paradise, released for the Famicom (the Japanese version of the NES), which was basically MonopolywithMega Man characters. It never saw a US release because Nintendo of America believed it would promote gambling among children. Also notable for being a Mega Man game that does not feature Mega Man as a playable character.
The Wily Wars—or MegaWorld in Japan—was only made available in the US through the Sega Channel, but when the service ended, you were out of luck if you were living in the US (unless you happen to have an emulator, or a Game Genie, which can bypass the regional lockouts of imported titles). The game saw an actual release—y'know, an actual cartridge—in Japan and Europe, but in a move that defied logic, it never saw that kind of release in the US.
Mega Man 6 was not released in Europe until after 19 years when it finally saw the light of the day on the Nintendo 3DS Virtual Console to coincide with Mega Man's announcement in Super Smash Bros. for WiiU/Nintendo 3DS. It almost didn't get released in the US either, as Capcom felt it arrived well past the NES's prime. Nintendo, however, published the game themselves.
Mega Man & Bass, or Rockman And Forte, which was one of the last games for the Super Famicom (the SNES's Japanese counterpart), having been released in 1998. It never saw a release outside of Japan until 2002-2003 when it was ported to the Game Boy Advance.
Super Adventure Rockman, an "interactive movie game" that combines text-based adventure gameplay with that of a First-Person Shooter and features Anime cutscenes. Notable for being much darker in tone than other games in the classic series, and as such was apparently disowned by Inafune himself, who thought it contrasted with the mood of other games a little too much.
The first game was originally intended to have eight Robot Masters like the rest of the series. When the decision came to cut the number down to six, only seven designs were fleshed out, and Bond Man◊, a glue Robot Master, had to be cut. Bond Man had since gained a cult following in Japan, and even Keiji Inafune has taken a liking to him. He was briefly under consideration to be one of the new bosses in Powered Up, but Inafune felt it would be better for him to remain mythic and unofficial. More information on Bond Man can be found here.
Putting aside Bond Man, you have the Robot Master fan submissions that were used as the basis for the new Masters from 2 to 8; there are roughly 750,000 Robot Masters who were at one point or another under consideration for the games. While some of the rejects got used eventually (see Development Gag in the videogame page), the vast majority of them are unknown to everyone who didn't directly sift through the postcards.
Only God knows how a possible opening sequence in Mega Man 3 would have looked like, but the slow first part of the title theme is a clear indicator that they had planned one for the game.
According to Mega Man Official Complete Works, the original concept for Top Man and his stage was lost when someone tripped over a power cord and the information hadn't been properly saved. It took three days to reconstruct it, and Inafune openly wonders in the book what things would have been like if the original concept survived (among other things, maybe the Top Spin wouldn't be a Joke Weapon / Lethal Joke Weapon).