I haven't re-bought anything I already own so far, but I think this may have to change. Windows XP has been good to me, but I'm going to have to upgrade to a 64-bit OS soon and that'll probably kill off half of my collection of games. I don't relish the thought of trying to install Myst: Masterpiece Edition or Syberia 1 & 2 on Windows 7. I had enough trouble trying to install Enemy Territory: Quake Wars and Half-Life 2 on my dad's PC with Vista.

So what have you bothered re-buying so far, whether it be to ensure compatibility with newer operating systems or to keep all of your games consolidated in one place?

This topic.

All of them. When available. And then some.

What can say? I like to support a good initiative, and I had rather use the GOG versions than the original disks. I still keep all the old disks and boxes, manuals and extras too, but more for sentimental reasons rather than practical ones.

Since I was but a wee when I first started playing any of these games, they're actually my first time purchasing them. All my allowances went to books.

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Duke Nukem 3D
Rise of the Triad
Earthworm Jim
MegaRace
The Incredible Machine
Planescape Torment

Arcanum
Beyond Good and Evil
Fallout Trilogy
Myst

However, I usually sell my retail copies once I buy the digital copy.

I own these in their original packaging and re-bought them on GOG:

Fallout
Fallout 2
Arcanum
Might and Magic World of Xeen
Under a Killing Moon
The Pandora Directive
Gabriel Knight: The Beast Within

Most of that was to avoid installation issues or to support GOG.

I own these on Steam from when I was a massive Steam supporter and have since re-purchased them on GOG:

Psychonauts
Arx Fatalis

I own a lot of other GOG games in their original packaging and have not re-purchased them, but might someday during a sale or when I want to replay them and have issues with the boxed copies installing.

I own PoP, BG&E, and Psychonauts for the PS2, but I have purchased the first two from GOG as well.

Syberia 1 and 2 are not repurchases for me, but they run just fine on Win7 x64 Ultimate. Myst (now there's a repurchase from a long time ago) can be more troublesome, but take a look at the workarounds found by this community over on the game forums. Also, Riven never gave me any trouble at all.

Under A Killing Moon.

And uh, I bought Duke Nukem 3D after buying Atomic Edition here. Does that count? :p

Myst
HoMM3

I'm thinking about repurching Fallout 1 & 2 just to put out some positive energy for my two favorite games.

Arcanum
Fallout
Giants
MDK
Descent 1, 2 & 3
Earth 2150 Trilogy

And probably a few more later.

I don't want to count them all but Arcanum, Planescape: Torment, and Baldur's Gate I have working copies of and I've bought them again here.

Duke Nukem, Blood, Torment, and Descent 1 + 2.