How can I get beer out of a keg without CO2?

There is an alternative way I have found to work. If you have your keg in a kegerator and have run out of CO2, then follow these steps.

First start by disconnecting the CO2 from the keg coupler. Use a bicycle pump with a needle used for blowing up sports ball to replace the CO2. Attach the needle to the CO2 line and use duct tape etc. to secure it.

Once you have made sure there is no leakage occurring, begin pumping and open the tap. The liquid will begin to flow out of the tap without the need for siphoning. As long as the bicycle pump stays attached with the CO2 line, this method will continue to work until the pressure is let out.

I agree with the above answers and think that is a very good method if you are using a picnic tap, but if your keg is at home and you can't pull it out of the keg and lay it on its side, this is a very effective method. I have used it multiple times myself when I didn't feel like going across town to refill CO2. If the need or opportunity arises, please try. If my given directions are followed, you won't be disappointed.

I would use gravity. Start by taking a liquid line with a picnic tap and filling with sanitizer. Next, put your keg on a counter. Take the lid off your keg (to de-pressurize). Connect your liquid tap to your keg, then open the tap. You should be good to go. Make sure to catch the first bit into a bucket, as you'll want to dump it since it has the sanitizer.

I would suggest using an autosiphon. Everything stays upright, and nobody's mouth is on anything. Rest it on the lip of bung until it gets down about halfway and then lower the autosiphon into the bottom. Really what you're looking to do here isn't that much different than racking from a carboy.

Similar to brewchez' answer, if you already have a picnic tap with a black beer-out disconnect on a long enough beer line, you should be able to syphon the beer out by filling the beer line and keeping the tap below the level of the beer in the keg. Obviously you'd also need the pressure relief valve open while pouring. You could start the syphon by either filling the beer line with water (or another beer), or sucking on the end of the tap, or gently shaking the keg with the relief valve closed and the tap open.

I've also heard of someone using a soup ladle to scoop beer out of the top of a corny keg, but I'd leave that as a last resort!

This probably isn't too helpful for your current problem, but they have small CO2 hand-chargers for corny kegs that use small CO2 vials.

This is one option.

I use one with a small picnic tap to bring a keg places without lugging the entire gas cylinder and regulator with me. You just have to be careful to monitor the pressure in the keg by feel. It also comes in handy if I run out of gas and haven't had time to get it refilled.

Put a cobra picnic tap and tubing on a grey gas IN connector and attach it to the gas post.
Attach a longer open ended piece of tubing to the beverage out post.

Lay it on its side with a 2x4 block under the end of it. Lay the keg so that the IN post is down at 6 O'clock and the beverage out post is at 12 O'clock.

Now keep the open ended running above the keg so beer doesn't run out of it. Then you can drain the keg as if it was a cask via gravity. Be careful about hooking up that tubing to the beverage out end. If the keg is charged/pressurized beer will come screaming out of it, so be sure the keg is laying on its side first, and have something to catch what beer might come out initially... I'd suggest a bucket, large glass, or your mouth.