ROCKMAN 5 ENDLESS / Capcom + Rock5Easily / NES
Rockman 5 Endless was inspired by the "endless" mode in Mega Man 9, but it differs slightly in that instead of being truly randomized it is just the best bits of each existing level chopped out and then thrown at you in random order, with a boss battle here and there to keep you on your toes. The game tracks how many rooms you have cleared and saves the high score.
Of course, Mega Man 2 or 3 would be the fan favorites to do this with, but I actually think Mega Man 5 is a pretty wise choice. It's unfamiliar to a lot more players, who kinda gave up on the series after Mega Man 3, yet it has the best levels out of the Mega Man 4-6 grouping. It also has some of the better music out of that group as well.
I think this actually makes the game more fun to play - you get straight to the challenging and inventive bits without dragging your way through the whole game, and you can play the levels with weapons you may not have had (you start with all of 'em) when you played through the game normally. This adds a little experimental and strategic touch to it.
The only downside is that once you've figured out the optimal strategy to get through each room, it can get a little repetitive, as you frequently see the same rooms over and over on repeated playthroughs. Still it definitely gets an A for effort at the least. Good job Rock5easily, this is a good one.
Oh, one last note - to play it you need the Japanese Rockman 5 ROM to apply the patch to. Apparently the English Mega Man 5 won't work. But the patch translates all the menus and such into English once applied.
* The patch
* Gameplay Video