o2 & MySpace or Orange & Bebo were among the most striking deals between European mobile operators and online social networking sites in 2007. Many have followed since then and a bunch of mobile-only players are also claiming to have great audiences.
Handset manufacturers have also embraced the trend and the recent announcement that Nokia would made a Friendster widget available (via Widset) on the brand new N79 is a good example of that. Not to mention m.facebook.com or the iPhone facebook app and many many others.
My colleague Julie Ask just published a very interesting report on this precise topic: Mobile Social Networking: Assessing Social Strategies for Carriers and Handset Manufacturers. A must read.