The only game I've ever intentionally bought two copies of, without getting it as a bonus in a compilation, is Mega Man Legends (Playstation and N64).

I own both Duke 64 and Duke Nukem 3D, but I got Duke 3D for free from GOG instead of buying it, so I'm not sure if that counts. I also barely bought Duke 64 for 25 cents at a yard sale. :P

For game compilations that incidentally happened to include copies of games I already had in a bundle, I have Mega Man 8 on Playstation and a copy of Mega Man Anniversary Collection on PS2 with Mega Man 8 in it, and Ocarina of Time and Majora's Mask on N64 and in the Zelda Collecter's Edition disc for Gamecube.

quite a few, I have bought several GOG games that I already owned on disc.

but probably the game I bought the most versions of is Resident Evil.

Long box,
Director's cut
Gamecube remake
and recently the PC release of REmake

I've got at least two copies of every Infinity Engine game (including on GOG), but I think the record is four copies of Baldur's Gate II. A compilation release of BG2&ToB, the Baldur's Gate DVD Collection, a GOG copy, and an original big-box that I found in a charity shop and couldn't resist. buying just so I could put it on a shelf and look at it.

Yeah, a good game that was killed by its bugs and bad release date.

There are quite a few. One fun one to point out: Daikatana. Yes, I actually have the retail and GOG versions of it.

PC:
Witcher 1 & 2 (hardcopies, then bought gog's also!)

Myst full series in hardcopy (they were rereleased & I got them as sets), then finally the gog.com versions of 1, 2 and 5... 3 Exile isn't available from gog, but I was able to patch it for win7 64)

Dune 1 (original floppies box as well as the mega-cd, which runs great in dosbox) if only I owned a MT-32 or SC-55 synth for its music output which is amazing with those units). Wish GOG sold Dune 1 already tweaked up properly.

Wii:
Xenoblade Chronicles!! - 4 ! (2 for me, 2 as gifts to relatives). Fabulous fabulous game design. Play it on big screen with or without dolphin. (Can't imagine it on a tiny 3DS screen, seems criminal to do tha!t, but at least it may get others aware of this as a great game.

Everything else, 1 each of many many treasured games in hardcopy and also many many digitally from gog!

Tangental:
I donI't buy Steam or Origin games because their DRM practices (or I'd own/play Dragon Age Origins and Bastion). And Steam passes some malware-laden games and doesn't care or refund.

I sometimes buy the "Special Edition" version after I have already bought and played the regular one.
In my case:
Forza Motorsport 2 Limited Edition - Xbox 360
Driver San Francisco Collector's Edition - Xbox 360
Forza Motorsport 3 Ultimate Edition - Xbox 360
Midnight Club LA Complete Edition - Xbox 360
Burnout Paradise The Ultimate Box - Xbox 360
Gran Turismo 6 Anniversary Edition - PS3
Gran Turismo 5: Collector's Edition - PS3
Driver: Parallel Lines Collectors Edition - PS2

Some games I've re-bought on console after playing them on Steam originally:
Alien Colonial Marines
Farming Simulator 2013
Just Cause 1 & 2
Legendary
Sniper Ghost Warrior 1 & 2

On PC the ones I have multiple copies of are those I originally bought on Steam but later bought DRM-free:
Euro Truck Simulator 2
the UFO series (afterlight, aftermath etc)
Shadowrun Returns
...and others

Shadowrun. It's just too good.

Many games here on GoG are games I own on disk. I also have Dark Souls PTDE on both PC and PS3. Final Fantasy X/X2 I have on both PS2 and PS3. Actually I have a few HD Collections of games I also have on PS2/PC. Baldur's Gate 1 and 2 on CDROM, DVDROM and GoG and I have the EE of both games on Steam.

Mostly it's for convenience or because the new version looks better or play better.

- Grand Prix Legends - Original Big Box & 2 "Sold Out" versions.
- Baldur's Gate I & II - Original & GOG
- Icewind Dale I & II - Original & GOG
- Planescape: Torment - Original & GOG
- Neverwinter Nights I & II - Original & GOG
- Fallout I & II - Original & GOG
- The Witcher I & II - Original & GOG (Although i haven't bought the GOG versions, it's the backup keys they sent me)
- TES IV - Oblivion - I bought the game in 2006 and then i bought again the GOTY edition just to get the expansions (it was cheaper that way)
- TES III - Morrowind (It came with the bundled games of my old graphics card but sometime ago I found the original cardboard version)

I've bought only two games on different platforms. One was Deadly Premonition. First, I stumbled upon a big discount for this game on Steam and I really wanted to play it. So, I bought the game. I downloaded it. It doesn't work. Then I go to Steam community forums only to find out that it's the same problem for thousands of players; Steam is still selling this crap and gives no money back to anyone.

Then I found Deadly Premonition on GOG. I bought it with a discount. Works perfectly! Thank you, GOG. So now I have two copies of the same game. One is a crap, another is good.

The other game is Beyond: Good and Evil. I had this wonderful game on a cd, as a hard copy. Years past, now the cd is lost somewhere back in my parent's house. And I bought this game here, on GOG. I couldn't be happier.

1). Myst series... back when it was new boxes (for newer versions/sequels bundling)... and then digitally from gog.
2). Witcher 1&2 and later from gog digitally for deals & more content.
3). Xenoblade Chronicles - 1 for me, then another for me in case anything happened to my first copy, and then 3 more as gifts for others. Yeah this is not my favorite rpg, ha ha!

Only 2 games in my case as far as I can recall
- HuniePop Bought it on Steam first, and then on Humble for the DRM-free version
- Doorkickers Again, bought this on Steam first and then bought the Humble version for the android version.

- Devil May Cry 4 & Devil May Cry 4: Special Edition
- Prince of Persia: Warrior Within PS2 and later the PC version
- Fahrenheit and later the Remastered version
- Saints Row: The Third on Steam then on gog
- Battle Realms retail, then gog
- Empire Earth Gold retail, then gog
- Unreal Tournament retail, then gog
a couple more that I don´t remember at the moment.

bloodrayne betrayal twice ps3 and steam

bloodrayne 2 steam version

skyrim twice pc and ps 3

colin mcrae rally 2005 3 times pc xbox and ps 2

jade empire added the origins version