Aside from being a company with a name that's dangerously close to copyright infringement, Macminicolo has long been dedicated to creating hosting solutions for Mac users. In fact, they only host - you guessed it - Mac minis. It's a pretty nice service. Just send them your mini and they host it for you and give you full access (it's all yours, not shared).
If you've thought about colocation but shuddered at the cost, this could be your chance. Right now, Macminicolo is running a contest to find the greatest answer to the question: "What would you do with a remote mini?" Start up a new business? Create a non-profit?
The contestant who submits the best answer will receive a year's free hosting, a Mac mini and a MacBook Air. As Jeff Probst would say, "Worth playing for?" Yes, Jeff, it is.
You can get the details here. Good luck!