There are certain advantages to turning off a water heater. If you just turn off the gas, then you don't have to worry about a gas leak while you're gone. If you turn off the gas and the water source, then you don't have to worry about a possible water leak, either. Of course, there are other sources for gas and water leaks, so that isn't the whole story (your hoses to your washer are more at risk for leaking). With an electric water heater, you'd save a little bit on electricity.
But there are disadvantages, too. First, you have to remember to turn the water heater back on - and wait for the water to heat up again. Imagine coming home at around midnight, unpacking the car, getting the kids off to bed and collapsing into bed yourself - but wait! You have to turn on the water again. And let's hope no one turns on a hot water faucet before you do otherwise you're going to have air in your pipes.
While the water cooled down and warmed up in the tank, it reached the "danger zone" of above 40 degrees and below 140 degrees for bacterial growth for more than 2 hours (cumulative). For people like me, who have well water and, thus, our water isn't chlorinated, the bacterial growth can be significant. This is one of the reasons we insisted that the thermostat on our water heater be set ABOVE 140 degrees even though a lower temperature would be more energy efficient.
Plus a big disadvantage is many gas utilities insist that THEY be the ones to relight the pilot light which means you have to wait for them to come out to do it. When we were in the 1989 Loma Prieta earthquake our neighbor went around and turned off everyone's gas (gee, thanks buddy - he was itching to use his special gas wrench.) We were tempted to relight our pilot lights ourselves but the utility company insisted we wait. It was a good thing we did because, while our furnace and water heater were fine, the vent to the water heater had fallen and, had the utility worker not checked it, we could have experienced a dangerous build-up of gas.
If we were going to be away from the house for more than a month, we'd probably winterize it (even in the summer) which is draining the water lines and shutting down the well pump, etc. A shorter vacation than that and it isn't worth the bother.