Super Mario Bros 3 - probably tops the list with over 50 playthroughs. Me and my brothers like to play randomized versions of the game and race each other. I often pick this up and play for short sessions just because.
Legend of Zelda a Link to the Past - around 25 playthroughs, similar situation to smb3, play and race with my brothers.
Resident evil 4 - something like 20 times across 5 platforms.
Fire emblem the Blazing Blade - 14 times but might be the game I spent the most total hours in since one playthrough takes quite a lot of time and I play and replay the same maps often.