Well from buying it to probably the release of the SNES & Super Mario World I probably played and completed Mario 3 on a near-daily basis... Mostly using the whistles to fast forward of course! Yes I love that game...
(play it far less now, but haven't stopped playing it!)
Secret of Mana, FFVI, Suikoden 1 and FF Tactics (almost forgot Link to the Past!) have had multiple playthroughs..
Recently, Spelunky gets fired up on a near daily basis ala Mario 3, I think I've racked up around 1200 deaths on the Xbox 360 version, and also have it on the PS4!
And I still play Adventure for the 2600 sometimes! It's the random Game 3 of course, love the fact that the placement makes some tries impossible to do, so usually plump for a best of 3, or 5, on my numerous seshes on it.
As a game series, probably Pokemon, but once I'm done with a particular game that's it, so I'm not sure that counts..