Yes, there are several products to do this.
There's CiteULike, which is completely web-based, has good support, allows you to share your library, see who has read which papers, which papers are trending in the last seven days, and has a good recommendation system.
I hate to say this, because I've always had good support from them, but its functionality doesn't really extend beyond that, and that's a problem: I was really enthusiastic about it, but I notice that I've barely used it in the last 14 months.
There's the Elsevier-owned Mendeley, where you can add people as contacts, and share what you own. Recommendations are also provided anonymously, based on overlaps between your library and other people's. It has a desktop application, which I have used, and a website, which I very rarely use.
There's zotero, which does allow you to share your bibliography with others, and to see who is sharing what. I found that it also insisted on duplicating all the pdfs on my local drive too, which meant I quickly uninstalled it.
And there's EndNote Web, which might allow libraries to be shared publicly, but I found the interface frustratingly unusable, so couldn't say either way.
In short, there are several applications which allow you to share the metadata of the papers you read, on the web. However, the user experience, ergonomics and functionality is patchy.