How can I safely work around power lines?

Call your utility company and have the power shut off at the pole for the duration of your work in that area.

Edit: As expected, some people don't like my answer. I have decades of electrical and electronic experience and I suspect those who don't like my advice do not have a solid education/experience in basic electrical theory and practice. However, I assure you that the wires are not as dangerous as popular ignorance imagines.

Climb up and have a close look at the wires you will be near. If the utility is on the ball, they will be completely wrapped in insulation with no exposed metal—except for the neutral—and the connections (between the utility wires and the leads to the meter socket) wrapped in electrical tape.

If the wires are old, possibly there is some cracked insulation, maybe even seriously cracked enough for some bits of conductor to be exposed. If cracking is serious or there is substantial cracking, call the utility and have them upgrade or wrap the wires. They should do this for free.

If the wires are in good repair, you can safely work alongside them, even while touching them. Respect them and keep all forms of metal away from them: no metal hammer parts, paint roller, crowbars, putty knives, wedding rings, wristwatch, etc. Use your fear of them to keep their position firmly in mind at all times.

If after working close to them and you still can't see yourself getting any closer, then by all means, call the utility and have them de-energized. This may require a permit and inspection, so it may be days before power can be reconnected. (I know permits and inspections don't make any sense, but the administrating authority is "just ensuring safety"—and making a living.)

If you were to fall off the ladder and the wires provided an opportunity to grab to save yourself, I would risk doing so. Probably the arresting force will bend the weather head, and might pull apart the electrical connection. After safely landing, keep the bare ends away from everything, and wrap them with electrical tape once you are steady on your feet.

It's simple. Don't let anything touch those power lines. If you're not completely comfortable being on a ladder or just don't feel this is your forte, then call someone who is. Life is too full of risks as it is...

I've worked around power lines for years as well as other people in this thread. I always plan my work around the power company disconnecting. They are mostly accommodating with scheduling and I have never been charged. If they did charge, I would completely be ok with it. Better safe than sorry. I'm not in a hurry when I'm trying to do a job safe and right the first time.

Also, Someone mentioned that planning to fall off a ladder was not DIY advice. I beg to differ. If you don't plan on the what if's, you'll not know what to do if you do by chance fall. If I ever plan on doing serious work on a ladder, I usually open windows close to the work area, and if their aren't any windows, I have D rings and a harness. caulk the holes after your done.

In my area hydro (aka the electric utility) will come out for free and a rubber "boot/sock" around the stack to the house; this is extra insulation around the wires, making it safe to work around. So, the electricity is able to stay on while work is being done! They sometimes take 2-3 days to come out, so plan ahead.

FWIW, I just talked to someone in the Austin, Texas Electric Distribution Department (Austin Utilities) and asked him about this. I am about to paint my house and I wanted to know if the utility company would turn off the power at the pole and what it would cost. He was a bit surprised at the question and said that people usually just paint around the weatherhead taking care, of course. He said that his workers just throw a rubber mat over the connections just to make sure. He suggested that I inspect the insulation first and if it's cracked, to call back and they will address that.

I grew up with the commercials that no line is safe to touch. So now I have to go up the front of my house where the power lines are I,ll be working off an aluminum ladder with the power lines directly behind my back, and if anyone thinks I'm not going to already have cmp wrap the lines I,m working around especially with a aluminum ladder,then your completely off your rocker anyone that gives u advise like go up and inspect the lines and if they look ok then go ahead and do what u have to do is just plain crazy and if anyone actually takes that advise then there crazier than the one that gave the advice. Always check with your power company before u do anything around but power lines. My idea if good advice is never carry our ladder straight up in case if power lines. My opinion