A Mac Mini is simply a small computer. It was engineered to have a small footprint on your desk and the trade-off is that it may have fewer I/O ports than other computers. Mac Mini's will also often have smaller or less capable processors, because of the engineering desire to eliminate the need for other space-hogging elements like larger heat sinks and or fans. My older PPC-based Mac Mini has been serving me very well for the past 5 years. I have it serving a number of web-sites (all fairly low traffic though) and it serves as a network fileserver and host for my Drobo.
So, just because it is small doesn't mean it isn't capable. It is. And, there is no reason to install Ubuntu as Matthew suggests, Mac OS X is fully capable to provide services like HTTP (web), Mail, FTP and other things we've become to expect. In fact, My Mac Mini has 2GBs of RAM and this is 4X the amount I would get in many cases for an entry-level hosting service online.
Finally, if the normal Mac OS X doesn't provide enough services for you, you can even install Mac OS X Server on the unit to get more enterprise-level services. I know of a hosting service that actually sells racks and racks of these to customers and they perform quite nicely as "servers", with a small "rack" footprint and power consumption.
I have a number of Macs and other types of computers here and no matter how old my Mac Mini gets, I still have good use for it. It is a work horse!