It might be a pretty cool feature to click on a user's name and see their shelf =)
It would also severely embarrass me because everyone seems to have more games than me (I have 4).
=D

This has already been suggested before, and there are appropriate ways to make a suggestion like this without creating a whole new thread on it. As sated in the FAQ I wrote a while back:
Please add *insert website feature here* to GOG.com.
GOG is currently in beta and will therefore be changing a lot as it develops. The GOG team is always looking for new ideas to enhance the experience and actually listens to the public when they ask for something. However, there are a few "proper" ways you can give the team your feedback. There is a GOG Features Wishlist thread in the general forums as well as the website feedback link at the bottom of the site.

whoops!
Sorry! My bad!

I wouldn't want that. I hope there would be a privacy option for that.

RABBLE RABBLE PRIVACY! RABBLE RABBLE!

I think the idea is kinda cool.

this. And I fully support this idea.

Maybe have it as a button under the avatar, if you've got the option turned on, you can see their shelf, if not, the button doesn't appear.

This would be most handy when it comes to gifting, but it's understandable that some people are not going to want it turned on.
My earlier suggestion was to have a 'friends' list. This would enable the shelf to have three options.
1) Private, unless granted access.
2) Friends access only.
3) Public.
1 & 2 have a bit of cross over, but depending on how things could be implemented would determine just how much information you want to give out.