Does such a thing exist? If so, which programs do this?
Only midi.
Where is the program that does this for MIDI? Or, can you name for me your favorite MIDI editor? Will said program print sheet music?
Pretty much any sheet music program. GuitarPro, Finale, TuxGuitar, others that I can't be bothered to think about.
Google NoteWorthy composer, you can just get the free trial. I don't think it really lacks anything that the full version has.