Stay way, way, way far away from them!! Seriously, distance is your friend and more is better, much better.

If that isn't really possible then you need to be very well insulated and not become part of the shortest electrical route to ground. Rubber is a very good insulator (assuming it isn't "contaminated" by a conductor or have any teensy tiny little holes in it.). In this case thicker (to a point) is better. If you have a choice dry is always better than wet. Voltage drops can be amazingly high even over short distances so keep feet close together (i.e. shuffle) and don't touch anything with your hands etc.

For local transmission lines (relatively low voltages say < 600V) a long length of dry rope (nonconductive) or dry wood (kiln dried preferred) along with some good rubber gloves and boots might let you move a line and live to tell the tale but I generally wouldn't have anything I would trust my life to in my home, much less in the car or in my backpack. Above that voltage level it really becomes a matter of needing the correct gear.

Realistically, I wouldn't trust anything I could buy at the local hardware store, lumberyard or super do-it-yourself store. There are places that sell certified inspected gear to linesmen (and I assume lineswomen). If you want or need to plan for this scenario you should find high quality (read that as professional/certified) gear specific to your needs and take the time to learn the appropriate/applicable standards along with the risks and techniques.

Personally I have decided the risk/reward and probability equation makes this something I won't ever plan for. Kind of like trying to figure out which wire to cut on the tamper resistant bomb some one left on my doorstep. I'll go down swinging but figure it won't matter which wire I cut, it will either work or I'll never know.

Please, please be careful around downed power lines.

- Eric