You'll need a media player or a PC, as rolli59 noted. WD, Seagate, Sony, and other have small media player boxes that are $80-$150 (without storage). Format compatibility can be a major issue, as can the network capabilities. If you're just using it to play back files from a directly connected USB drive, you won't have to worry about how well (or bad!) the network features work, BUT, be sure to check out reviews as some players don't work well with some of the file formats they claim to support.
Another option is the new micro PCs that are coming out. They typically use netbook processors that are a bit weak for full-fledged PC use, but work well with ION2 or AMD graphics for HD video playback.