One of the biggest annoyances for anyone that likes to shop around is the decentralized library of games that can sometimes be locked away behind a dozen accounts, each one hosting only a small portion of the games, yet completely sealed away from all the others.
While GOG's Connect service doesn't offer a final solution to this whole mess, it is a rather nice gesture as it allows you to link your Steam and GOG accounts together in order to import a variety of games from your Steam library into your GOG one. Here's a list of the currently eligible games:
• Bit.Trip Runner
• Braid
• Breach & Clear
• Breach & Clear: Deadline
• Broken Sword: Directors Cut
• FTL: Advanced Edition
• Galactic Civilizations III
• Mount & Blade
• Project Zomboid
• Saints Row 2
• Shadowrun Returns
• Sherlock Holmes: Secret Of The Silver Earring
• The Witcher: Enhanced Edition
• The Witness
• To The Moon
• Trine Enhanced Edition
• Two Worlds
• Unreal Gold
• Unreal Tournament GOTY Edition
• VVVVVV
• Xenonauts
This offer is only going to be valid for the next five days, so make sure to import all of the games as soon as possible, and don't worry, you'll be able to keep both the GOG and Steam copies once the offer runs out.
The one potentially problematic feature of this transfer is the fact that your cloud save files will not be copied over to GOG due to Steam's built-in security features that prevent websites from snooping around your account. In other words, if you plan on playing your GOG version on a different PC make sure to copy over the safe files as well, or be prepared to start from the very beginning.
If you're interested in all of the nitty-gritty details I'd recommend you head over to the official FAQ.