For me:
Water — well pump turned off.
Gas — not applicable, but I would leave it on; definitely so in the winter so the furnace will run.
Electricity — absolutely left on. No sump pump means DrewE's basement may become a giant wading pool. No furnace means DrewE's plumbing may freeze (in winter time). No refrigeration means DrewE's frozen foods would go bad. No power to the answering machine means missed phone messages.
Water heater — sometimes turned off, sometimes not. Modern water heaters don't lose too much heat when there's no water draw, but there's no real drawback to turning it off either. For a long time away, I'd likely turn it off.
Thermostat — turned down to 45 or 50 in winter, left off in summer (no central A/C, no real need for it here in Vermont).
My house was built with electric heat, with an oil furnace added at some later time. When I am away during the winter, I leave the electric heat in the bathrooms on but set very low so that, if the furnace stops working for some reason, the pipes will hopefully remain above freezing. Of course, it doesn't actually turn on so long as the furnace is doing its job.