Excluding NES classics like the SMB series and Contra for example which I've probably beaten each a hundred times over, I've completely finished A Link To The Past at least a dozen times, got all three paths of the original Star Fox multiple times, went through Super Mario RPG 3 times, and 100% completed the original Banjo Kazooie and Super Mario 64 at least 5 times each.

Majora's Mask beaten it about 8-9 times, 3 of them being 100% completion. Still my favorite game.
Fire Emblem Awakening 4 times
Fire Emblem Radiant Dawn 3 times
Golden Sun +Lost age 3 times for both.

I've played and completed Paper Mario and Super Mario 64 at least 4 times each.

Halo 1 more than 100 times. Halo 3 pretty close due to Coop campaign. Also this gen Ryse Ive already done like 6 times?

Metroid Fusion and Zero Mission. I'd take the cartridges with me on car trips along with multiple gameboys, and I'd keep playing to my heart's content.

i think Starfox 64. since it was pretty short.

Final Fantasy 8 (like 15 times)
Bullet witch (its only 4-5hrs long so its not really an achievement)
FF IX (10 times)
Yoshi Island, Mario world and Mario 3 (a loooot)

Pokemon FR/LG or R/S or SMB3. Ive replayed all of these games so many times that I cant remember :p OH! And FF3 DS! I love that game (its so underrated, people really dont appreciate FF3 v.v)

I play every game just once, even if it has multiple endings.

The exceptions are the following games, those are my favorite of all time: Numerous Tomb Raider games, GTA San Andreas and Vice City and Resident Evil 4.

Over 10 times each:

Maniac Mansion
ZakMcKracken
Indiana Jones and the Fate of Atlantis
Monkey Island 1 - 3
Day of the Tentacle

These are short games, but where do you take the time to play long RPGs like Final Fantasy games that often?