Are there any torrent clients that run as a service?

Look at Hadouken, it is a BitTorrent client for Windows which runs as a Windows Service. It is also free and open source.

Disclaimer: I am the author.

uTorrent definitely works as a service (I use it), and there's guides out there (need I say google?) if you have some preference of client, try searching "install some_bittorent_client as a service"