Two US states do not observe daylight saving time: Arizona and Hawaii. Most of the other states change their clocks seasonally under the federal rules established by the Uniform Time Act.
Arizona generally remains on Mountain Standard Time throughout the year, although the Navajo Nation within Arizona does observe daylight saving time. Hawaii stays on Hawaii–Aleutian Standard Time year-round. Its tropical location means seasonal daylight changes are relatively small, while Arizona’s hot climate has often been cited as a reason to avoid extending evening daylight and potentially increasing cooling demand.
The answer is two when the question asks specifically about states. Several US territories also do not observe daylight saving time, including Puerto Rico, Guam, American Samoa, the Northern Mariana Islands, and the US Virgin Islands. Those territories are not states, so they are excluded from the count.
Arizona’s exemption took effect after the state adopted daylight saving time briefly in 1967 and then opted out in 1968. Hawaii opted out under the Uniform Time Act in 1967. A frequent error is counting territories alongside states or overlooking the Navajo Nation’s local exception.