Acoustic Audio 10 inch home theatre powered subwoofer use speaker wire or subwoofer cable?
As you used the phrase The wire that was included for the subwoofer, I'll presume that we're talking Home Theater in a Box here. As someone above mentioned, sub frequencies can use a lot more energy. In a larger system where you are consistently running several hundred watts over longer distances, a larger wire would probably be benificial. For a HTIB system such as yours the wire that came with it would be more than adequate over the short run that would typically be needed. Having said that, there is nothing wrong and nothing will be damaged by going to a larger gauge wire. Just not a lot of benefit.
Use a long RCA cable. If you use speaker wire - you have to run wires from the left/right outputs to the sub, then more wire from the sub to the left/right speakers. Then you have to tell your receiver your left/right speakers are LARGE and you do not have a sub to get things to work. A single long RCA cable is simpler. You can even make your own with pre-terminated CATV coax and some F-to-RCA-Male adapters from Radio Shack. Subwoofer signals work fine and do not need any kind of higher end RCA cable.