The following I know for certain
Resident Evil Remake (GCN, PS3, PS4)
Resident Evil Zero (GCN, PS3, PS4)
Resident Evil 2 (PSX x2, PSN, N64, Game.com)
Resident Evil 1996 (Saturn, PSX x2)
Resident Evil 4 (Wii x2, GCN, PS2, PS3 x2 NA/Japan release, iPad too, lol)
Resident Evil 3: Nemesis (classic) (PSN, PSX x2)
Resident Evil 5 (US, Japanese Gold version, PS4 version)
Resident Evil: Code Veronica X (PS2 x2, PS3 NA/Japan, PS4 (though it's the inferior PS2 PAL release))
Resident Evil Revelations (Revelaitons version on 3DS, Wii U, PS3)
I'm sure there are others but can only think of double dipped, not triple dipped.
edit - Holy shit, that totals up to 35 times. iPad and Game.com technically don't count so taking out the initial purchase of each title, I've rebought various RE titles 24 times, and that doesn't even count the games in the series that I've bought twice or once. I've probably bought RE titles upwards of 40 times in my life, lol. Never really thought about the overall totals prior to this thread.
Thanks OP, I know realize that I'm a huge fucking nerd because of you!