Thanks for the help folks. If it is indeed a power line, I don't think it's live because I (rather foolishly) fiddled with it hoping that it was a phone line. A couple people mentioned a satellite hookup - ironically enough, that's what I'm dealing with. I'm pretty sure no previous owner ever had a satellite system, but I can't be sure. We've had our DirecTV setup in this house for about 6 years, but we never hooked up the phone line (not completely necessary if you don't order pay-per-view shows). We recently upgraded to a Tivo-equipped receiver and you need the phone line to activate your DVR service. I had always assumed that the wire was a phone line, but when I went to install the jack, I was baffled by the wire internals.
The only other clue I found was this: in the basement I can see two grey wires that look to be the same gauge running parallel. The come from the finished part of the basement (so I can't see where they really terminate) and run towards the family room, but disappear up into the insulation and wall framing. If one of these is the "mystery" wire, I'm not sure what the other one is for.