There is rust right above the gas flame in our water heater (not outside the water heater as in this question Rust spots on water heater -- time to replace? or on the inside where the sacrificial anode might be an issue). A repair guy said this indicates a slow leak that could become a big problem all of a sudden, and that we should probably replace the water heater. The water heater is an American Water HEater Proline model and it is about 12 years old. Should we replace it?
I've never seen a burner assembly area that wasn't rusty, H2O is a byproduct of combustion. Things to consider: is the exhaust vent in good condition, is the TPR valve not leaking and in working order? Provided it's not in a location where a catastrophic leak would cause damage, ride it out. That being said, 12 years is getting towards the end of its life. If, at some point in the next few years, a few days without hot water is unacceptable, replace it soon or begin saving money now by upgrading to a tank-less.