If you count up the number of times I've finished each level, I think Lode Runner for the Atari XL/XE computers would win. Brilliant game. The levels you could create with such a simple toolset!
In terms of straight-through, beginning-to-end, no-cheats - should I be admitting this? - probably Bubsy for the SNES. This is all the more impressive when you realise it had no save-game facility, and I was a bit of a completist, so finishing it was an all-day project. Plus, we had Super Mario All-Stars, so I had better platformers to play. Yet every so often I would get an itch to play Bubsy, and commandeer the SNES for the day to run through it.
(Incidentally, I was so excited when I realised the Mike Berlyn of Infocom fame was the same guy who created Bubsy.)