I know this is probably a dumb question, but here goes. I want to uninstall a game from my computer (to make room for other games). Trouble is, I don't want to lose all my progress. Does GOG.com save the progress of games that I have purchased in my library or should I resort to an external hard drive?

/If you're using Galaxy and the game is cloud saves friendly then yes. Otherwise pay attention while uninstalling the game, the installer should ask about keeping or deleting game saves.

If you're using Galaxy and the game supports cloud saving and your cloud isn't full (1GB max) then your game save SHOULD be backed up. But I don't trust cloud saves on any service. On another note, uninstalling most games won't delete their saves unless you tell the uninstaller to do so.