Can I fish electrical down to the basement to add a new outlet?
Electricity doesn't care much whether it runs vertically or horizontally (it really only cares how far it runs).

Often the easiest way to add an outlet or switch is to run it down through a basement or up through an attic. So long as the cable is properly buried in the wall cavities and you don't unreasonably compromise structural members, there should be no problem.

This assumes, of course, that you are not overloading a circuit, that you are using the proper gauge of wire, and that any exposed cabling is in a permitted area (usually an unfinished basement or attic is okay under most local codes).  You also need to make sure cables are properly tacked down and not subject to damage, and that as you drill, you are not hitting other cables, pipes, or leaving hidden cables too close to a surface where they might get damaged in the future.