I suggest that you run it with a load every three months. Run at least until the engine operates at full temperature for ten or more minutes.
Running it benefits the engine by burning off moisture, etc.
Running with a load ensures that the exciter will stay ready for action. Some use capacitors and, should the capacitor discharge completely over time, the exciter won't set up correct flow in the alternator. This preventative running does not have to be a heavy load. Even a few seconds with a light bulb on each phase will prevent exciter problems.
But...
The unit should occasionally have a load close to its rated Running Load Current. This helps burn off junk in the engine and the alternator's oxidation. I do this once per year on my portable. I do this with both the portable and with the large (up to several megawatt) units in my job. The process is called "Load Banking".
And, of course, follow the engine manufacturer's recommendations regarding maintenance like oil changes, filter service, etc.
Arch Mortar mentioned fuel stabilizer. I like Star Tron for my gas portable, but do replace the stored fuel every six months. (Dump it in the car where it gets diluted.)
If you're speaking of a portable, have you considered converting it to natural gas? You take a small decrease in capacity, don't have to make trips to the gas station- assuming the roads are passable. Many kits are on the market for most brands.
If you are speaking of a whole house unit with an automatic transfer switch, it is critical to use the transfer switch periodically. The best way to do that is to disconnect utility power so it transfers. There is usually a circuit breaker or fused disconnect you can turn off to simulate power failure. I get a lot of emergency calls from hospitals & other critical installations because the transfer switch didn't switch.
