I am working on a social networking site like facebook and I need my users to reach their webmail address book contacts to invite them to the site. My website is prepared by ASP. Do you know which is the best company who sold this feature??

I think it all depends on what webmail feature you need to access, every user may have a different one, so it's highly unlikely that you will find one that works with everything.

Have you not written a messaging system as part of the project?