Either Dead Rising 1, which I bought three times (once because the original box I already had was kinda ruined, and the other one because it was the platinum edition), or almost any game with a GOTY edition, such as Dark Souls, Bloodborne, Oblivion, Red Dead Redemption... and so on. 

WINNER!!! :P

OT:  FFVII would probably be my most with PS1, PC (original Eidos version), PS3/PSP on PSN, PS4 on PSN and you can bet ill be getting every one of the remaster versions :D

FFX and X-2
PS2, PS3, PS4, PSV and PC.

Odin Sphere. OG PS2 title, PS2 Classic for PS3, Liefthrasir for PS4, and Liefthrasir for Vita.

Dragon Quest 1. I have it on NES, Famicom, SNES Repro Cart wiath DQ 1&2, GBC, and Android/iOS.

FFVII bought 3 times.
FFVI 3 times
Suikoden II 3 times

A huge amount of games bought twice.

GTA IV! The stupid 360 kept creating those rings on those games, and I never shook the console!!! Eventually the 4th disk finally became the lucky one, and it hasn't had any problems since.

Resistance 2 - the first disc broke, bought a replacement because I played it online all the time.
God of War 1 - had the games on PS2, bought the collection for PS Vita.

I almost bought Uncharted 3 again, in the Nathan Drake Collection. I did not had UC1 and 2 and the price was decent. However, before buying it, a PSN flash sale put each UC game for 7 dollars, so it was a no-brainer to get them for PS3 there and I ended up not buying the collection.

I don't buy the same game again for GOTY editions or to have it on multiple platforms. I'm not putting my money on the same thing twice. Buying a replacement is reasonable. I also thing that buying collections is a good decision even if you already have some of the games included, as soon as the collection is cheaper than buying the remaining games.

Super Mario Bros. on NES, All Stars SNES, Deluxe on GBC, Wii VC, Wii U VC, 3DS VC, All Stars Wii Port.

Uhm... Let's think out loud here. It's got to be a Zelda game because those are pretty much the only ones I have multiple times. There's a couple I have twice or maybe three times, usually the original and a remaster or the original and a port to mobile/later console.

But yes, let's see here;

The Legend of Zelda Ocarina of Time (N64)
The Legend of Zelda Ocarina of Time LE (Australian Gold version) (N64)
The Legend of Zelda Ocarina of Time 3D (3DS)
The Legend of Zelda Ocarina of Time 3D with LE 3DS console (3DS)
The Legend of Zelda Ocarina of Time on Zelda Collector's Edition (GC)

The Legend of Zelda Link's Awakening (GB)
The Legend of Zelda Link's Awakening DX (GBC)
The Legend of Zelda Link's Awakening DX (GBC) (replacement)
The Legend of Zelda Link's Awakening DX (3DS VC)

Yeah, it's Ocarina of Time. I have it five times, though to be fair the Collector's Edition isn't really a retail purchase, so taking away that one it's tied with Link's Awakening at four purchases. I have a lot of the other Zelda games, like LoZ, AoL, ALttP, MM and TP, three times.

EDIT: Unless we're going to count the original Super Mario Bros. and the Super Mario All-Stars version as one: NES (original), SNES (All-Stars), GBC (Deluxe), Wii VC (original), 3DS VC (Deluxe)