Do I need a permit to replace a water heater?

Usually, yes. The model IRC requires a permit to replace a plumbing, gas or mechanical system (R105.1), and its list of permit-exempt work doesn't include a water heater swap (R105.2).

Section R105.1 of the 2021 IRC says anyone who intends to install, alter, repair, remove or replace an electrical, gas, mechanical or plumbing system that the code regulates must first get a permit from the building official.

The exemptions in R105.2 are narrow. On the plumbing side they cover stopping leaks, clearing stoppages and repairing leaks in pipes, valves or fixtures, as long as the repair doesn't require replacing or rearranging valves, pipes or fixtures. The gas and mechanical lists cover portable appliances and replacing a minor part that doesn't change the equipment's approval. A new water heater isn't on any of those lists.

The replacement still has to meet the code for the parts that make a water heater safe: the temperature-and-pressure relief valve and its discharge pipe, a drain pan where a leak would cause damage, combustion air for gas units, and an 18-inch raised ignition source in a garage.

Birmingham, AL example: the city's 2024 Technical Code requires a permit to install or replace any plumbing or gas system it regulates (Section 103.1.1). The owner of a single-family home may do their own plumbing under conditions, but still has to get the permit and inspections (Section 101.3.5). Gas work isn't part of that homeowner allowance (Section 111.6). The city's minimum charge for any permit is $125 (Article V).

Rules vary by city and county, and some, like Birmingham, replace the IRC's permit chapter with their own. Call your building department before the old tank comes out.