Gas heaters thermostats use the fusable link method. Electric stats use whats called a "bi-metal disc" high limit. In either case, the high limit should open if the temperature exceeds 180 degrees. Should is the key word. After the high limit, of course you have the T&P, which should blow when the temperature exceeds 210 degrees. Should. The problem is that things fail. Thats why they want you to trip the T&P each year to make sure the mechanism isn't clogged or "rusted" shut. Like Jad said above, it usually results in letting some junk get under the seat and then the T&P will leak.
Do you replace the T&P and stats frequently? Its a good question. I'd probably recommend that you at a minimum trip the T&P to make sure it is not jammed up, and be ready for the leak that is likely to happen. If your heater is in good shape, and the stats remain in a nice clean moisture free environment, then they should be fine for years to come. Trouble with the stats usually shows up in the form of a tripped high limit. There is only one thing that trips a high limit. HIGH TEMPERATURE. That's the clue telling you to look for a problem, and fix it. If no problems can be found, REPLACE THE STATS. Period. I am constantly amazed at how many customer say they have been pressing the "red button" on the water heater now for months. The high limit reset is to be used once only, so you can have hot water while you wait for service. It will trip again, at least you hope it does... otherwise you have just started the countdown to potential "launch".
On the used heater, I definitely concur that the T&P and Stats should be replaced. The elements should be checked for grounding too. Stats can be replaced without draining. Just try to get the same style stats so the wires will reach.