I've refi'd twice now (2004, 2011) via Lending Tree, online. The competing offers came in fast and were for lower rates than my local banks. Plus, I was able to get cash out, which local banks were not willing to do.
There was a lot of phone, email, and fax work, but not any more than I would have had locally, I suspect. I handled it all from work (between the message boards and the refi, I hardly see patients any more
), so I would have been on the phone/email/fax to a local guy just as much, I think. The lender I seleected had a loan processing person who was my primary point of contact. He was very proactive and responsive - a real go-getter, in a good way. No complaints.