Colocation facilities are typically stuffed full of various rack-mounted servers running all manner of websites and other tasks with fat pipe connections to internet backbones. One company, MacMiniColo, offers colocation services and is dedicated to hosting Mac mini servers. Long before Apple introduced the dedicated Mac mini server a year ago, MacMiniColo has been setting up all flavors of the headless Mac for customers.
The Mini makes an excellent server thanks to its compact dimensions, low power consumption, good reliability and reasonable power. Servers don't generally need a lot of inputs and outputs, just a fast ethernet connection -- and the Mini server comes with a gigabit port.
MacMiniColo currently has a promotional deal available that expires tonight, at 12 AM Pacific Time (so if you want to take advantage of the offer, head to MacMiniColo's site now). You can get six months of colocation service for your Mini for just US$10 a month with 200 GB per month of bandwidth. After the first six months, pricing reverts to one of the regular plans that start at $35 per month. That should be enough time to try it out and see if the company can meet your needs. TUAW's Steve Sande used MacMiniColo for some time. You can either send in your existing Mini to the data center in Las Vegas or have MacMiniColo provide one for your needs.