A mixture of their being cool people who want their customers happy + it being a good PR move that will generate lots of goodwill for GOG and the participating publishers (and some misplaced goodwill for Valve, who had no part in this, save making the API available for anyone to use).
I would imagine GOG is probably also taking note of what people have in their Steam libraries, too, in order to help them decide which of those games (or similar games) that they don't yet sell here they might want to try getting, and probably other uses, too. World domination, at some point, I'm sure. =)

It's all very very sinister........:)

I did this.
It's a small initiative of GOG along with publishers so that you don't buy same game twice.
I love DRM-Free revolution and hence I love GOG.
Almost all my DRM-Free games are on GOG (rest of them are in humblebundle).
I love GOG connect as well because the price of steam game in my region is one fourth of that on GOG.
And GOG don't support my currency.
So people from my region can enjoy DRM-Free goodness without downloading anything from steam.
It's also a better option if you keep buying 1$ bundles.

There is no catch.
It's hassle free.
Just connect your steam and GOG account, press refresh and voila! Your games will get added.
It takes even less time from buying or redeeming a gog code!!!

Yes it's a marketing strategy.
They are doing this because what my friend HunchBluntley said!!!

Why would there be a catch? Paranoid much?

It's also a way to help people move away from steam, where "all their games are", by giving them the same games here.

Dat rhyme.

I've used it several times now. For me as a user of both stores, it's a great service. I love now actually owning DRM free versions of some of the games I originally purchased through Steam.

As far as marketing goes, I guess GOG uses it as an incentive for Steam users to also have a look here, and also to gain more knowledge about their user base.

Steam's cancerous userbase invades gog periodically?

Because businesses are not known for being altruistic. If a business does something that happens to benefit their customers, you can be sure that the business also believes that there is a benefit for them as well. Sometimes, as with 'free' stuff on the internet, the initially non-obvious benefit for the business turns out to be something anti-consumer, like advertising, making the 'free' stuff much less appealing. This has conditioned at least some of us to look for what the catch is, where we get free stuff but the business benefit is not immediately apparent.

Nothing paranoid about it.

No catch - just nice and reliable stats for GOG to see exactly what their audience have in their Steam libraries in exchange for a free GOG library update.
While there is data from steamspy, it's not specific for the existing or the possibly interested GOG audience, so GOG is better off with this data.
Win-win.

No catch really. It's just GOG's version of handing out free Steam keys to previous owners of the game, except for Steam you have to get them through the publishers but for GOG the existence of the Steam Authentication API allows them to do the handing out *for* the publishers in an easy automated way.

Their benefit is doing the same thing that made Steam grow so fast over the years (and piggybacking on that success by having those people use their large Steam libraries to grow their GOG libraries). Basically the more games people have on GOG the more 'invested' they become, the more likely they become to make some, more future purchases. On top of that, the more activity GOG gets the more it will draw in other people through social networking. And of course on top of that it puts GOG in the spotlight every time they advertise more games for GOG connect.

Nope, definitely paranoia.

Well, this *is* GOG after all. It has it's fair share of people who are here because of some paranoia or another, usually related to DRM or being tracked by clients. (no not saying all paranoia surrounding DRM was unjustified, but the extremes some think about are still extremely unlikely occurrences)

you should take a closer look at these forums before thinking people here are all that superior.