It is often quite difficult to remove an anode rod, especially because merely putting a wrench on it provides no leverage. So when you try to turn the anode, the tank turns, too.
People have inquired about using penetrating oil or other solvents. We advise against this, since the stuff could seep into the tank and we don't think that drinking or bathing in solvents is especially healthy.
However, there are several strategies that offer a good chance of removing stubborn anodes. Before we start on them, there is something you can do to improve your odds of success. If the anode is the hex type, which most of them are, then you will need something attached to a 1 1/16-inch socket. These sockets come in 6- and 12-point. The 12 is easier to use, but the 6 gives a better bite. You can improve on that by filing the bottom of the socket until it is totally flat. If you round off the hex nut on the anode already in the water heater, you've blown it. Nothing more to do except wait for the heater to rust out and replace it.
As to getting them out, here are some possibilities.Impact Wrench
For a lot of folks, it's probably not worth it to run out and buy a new piece of equipment just to remove an anode, but for those who already have one, or can rent one, an impact wrench can be quite effective.
Just remember that you only want to use it to loosen the anode, not to tighten it. Indeed, you'll want to merely break the anode loose, then loosen the rest of the way with a socket wrench, so as not to spin the hex head and probably knock the rest of the anode around the inside of your tank.
You'll want to tighten manually. That will give you better "feel" in case you're starting it wrong and will prevent you from hopelessly stripping the threads. And be sure and use pipe-thread seal tape.Opposing Wrenches
Another technique that will work either with hex anodes or combo anodes or nipples is to put one wrench with a long handle in the counterclockwise or loosening position on the anode or nipple you're trying to remove, and place another, similar-sized one on the other nipple in the clockwise or tightening position. If you place the wrenches so you can squeeze them together, it will give you a lot of leverage against the tank itself.Tap, Tap, Tap
Another strategy is to put a wrench with a long handle on the anode or nipple you're trying to loosen and tap it repeatedly with a fairly heavy mallet.Back and Forth
A final possibility is to try tightening the fitting a little to see if you can get any movement in that direction, then loosening, then tightening, working it back and forth to get an increasing amount of play that will eventually result in loosening.Preventing Nipple Collapse
This is not a method. Rather, it addresses an issue regarding water heaters that come with a combo anode in the hot port. Putting a wrench on the nipple that is integral to the anode could break it if it is very tight. Putting something inside the nipple, such as a bolt or another piece of pipe will allow you to put full force on a wrench without having to worry about catastrophe.