Super Meat Boy Forever

After you beat the boss of the 5th world, Omega Alpha, there's an option in the save select menu to enter New Game +.

It took me a little while to notice it, but it's at the bottom of the screen when you have the selector on that save file and can be activated by pressing the start/pause button.

Then all you have to do is playthrough the game and beat Omega Alpha again. This is also a good way to get more bandaids (Edit: Pacifiers) and access warp zones that didn't show up or were too hard to find in the last run.