As someone who has a decent amount of experience with all three, let me give ya' the lowdown on 'em...
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GoG:
+Decent selection of games if you're into older titles. They don't have it all, but they do have some great classics.
+No DRM whatsoever. No restrictions or anything.
+Most games are packaged and tweaked in such a way that they will run without needing to hunt down fixes and such
+I personally haven't encountered a single game that I bought from GoG that didn't run.
-Pretty much isn't recommended for new stuff at all, unless it's an indie title.
-Isn't as convenient as Steam and Origin, since GoG's downloader client is... just that, a downloader client which still requires the use of a browser.
Steam:
+The premier digital distribution service, thus it's very well supported
+Massive catalog of games, both old and new
+SALES. Oh god the sales. So many great discounts to be had...
+Plenty of awesome community features integrated into the client, such as forums and chat and the ability to track the activity of your friends and easily join multiplayer games with them... and so on and so forth.
+All of the above community features can even be accessed while playing most games through the Steam Overlay, which also has a web browser in case you don't want to alt-tab for that.
-Still can be a bit glitchy, at least it is for me
-Not all games are packaged or tweaked in such a way to make them run. Many older games still require you trying to find fixes or do some tweaks and such on your own.[footnote]A prime example of this is the Steam version of Wolfenstein 3D. It comes with DosBox so you can play it, but by default DosBox isn't properly tweaked so you can have the best possible framerate in the game. You have to manually go in and do it yourself if you want the game to not chug as if it was being played on a computer that was outdated even by 1992-standards.[/footnote]
-Related to the above: it is very much possible to buy a game on Steam that won't run on your computer at all due to some sort of issue. This has happened to me personally, too.[footnote]... don't buy the original Far Cry if you have a 64-bit version of Windows 7. Some people claim they can get it to work, but I never have been able to.[/footnote]
-SALES. They will drain your wallet so fast you won't even know you had money to begin with.
-Technically still is DRM, and games bought though Steam might even have third party DRM like Games for Windows Live or UPlay as well.
Origin:
+Pretty much is Steam, but run by EA and with a new skin.
+Is more stable than Steam, at least in my experience
+Has very quick download speeds
+All games I've purchased through Origin have worked on my rig. Might have needed some tweaking still, but I don't have any games that won't run at all.
+Not nearly as horrible as people make it out to be. Seriously...
-While pretty much identical to Steam, it's slightly less polished
-Community features aren't as good
-Possibly the smallest selection out of all three
-Technically still is DRM, and still can have third party DRM tacked on alongside Origin's DRM.
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Out of all three, I prefer Steam the most. But all three are perfectly fine and work well in my experience.