Well, it depends on what you're planning to run off the powerlines. A few streetlights or interior lights ought to be fine, but something like a motorized bridge would probably be right out. CAT-5 cable works out to a little less than 3 1/4 inches in HO scale with the insulation, which I'd estimate to be about the right size. Stripped CAT-5 (which probably wouldn't be easy to do) might be about right for N scale. Another method I've seen used is solder. The thin stuff is about the same diameter as insulated CAT-5, but is all metal (though I don't know how much the resistance would be over a sizable length). It's soft, so it's easy to form droop. I don't see what would stop you from running connections from it to lights or what have you.
I'm sure you'll get people saying to don't run power over scale power lines, but I sure as heck won't. I've thought of doing it myself to eliminate wire runs from yardlights to the ground, but got lazy. Go ahead and try some CAT-5 or light solder and let us know how it works!