Depending on where you are, but: OVH is known to offer dedicated servers with very generous bandwidth allotments for very little money. E.g. their Dutch budget brand http://www.isgenoeg.nl offers a basic server with 5TB, then 10Mbps bandwidth for EUR 15/month, and their UK http://www.kimsufi.co.uk/ is similar.
(No personal experience, offer seems valid for nationals only, WebHostingTalk suggests there's little support, OVH apparently change their upstream providers all the time to get the best possible deals - you get a lot of bandwidth but latency varies from day to day. Seems acceptable for a simple file server.)
(No personal experience, offer seems valid for nationals only, WebHostingTalk suggests there's little support, OVH apparently change their upstream providers all the time to get the best possible deals - you get a lot of bandwidth but latency varies from day to day. Seems acceptable for a simple file server.)