Gaming consoles like the PS3 and Xbox 360 are a great start for both video and music, you can use either internal HDD storage or an external USB HDD as well so no server is required. They both support UPNP/DLNA so if you wanted to use a computer to stream the files. I would say their interfaces are lacking for larger libraries.
I would highly recommend an Apple TV for anyone that wanted both video and music over the PS3 and Xbox 360 just mostly on the ease of use and library selection. Like the PS3/Xbox 360 you have both internal storage and can stream, but no external USB support. Remote works, but an iPod Touch is faster with large libraries. Also i've noticed that the technically challenged folks will use the Apple TV over the PS3..
With any video server you will hit limitations on video codec settings, and can get rather annoying, but this seems to be less and less of a problem now that everyone seems to support h.264.
Another option is to hack an old xbox or find something that can run boxee like what dlink is coming out with. I'm sure more well post with other alternatives..