My native state is Indiana, so that would be "Back Home Again in Indiana".
I lived for a while in Virginia. The "new" state song (10 years) is "Our Great Virginia". The old one was "Carry Me Back to Old Virginia", which didn't please everyone.
Michigan, where I lived for some years, has two songs: "My Michigan" which is technically the official state song but is almost never played and "Michigan, my Michigan", which is the one that most people consider the state song.
My current state (Florida) for almost the last 50 years is "Swanee River (Old Folks at Home)" by Stephen Foster. Now, it's really the Suwannee River, but that extra syllable didn't fit well into the song. Strangely enough, Foster never saw the Suwannee River but he liked the sound of it. Also, there were some lyrics that aren't exactly PC by today's standards, so there have been some "adjusting" there.