No need to limit yourselves to your own state, despite the thread title.
Do people think that he deserves to supplant Bill Clinton?
Walt Disney was born in Chicago, but always called Marceline, MO his home town.
Maryland here. Who’s more famous, Babe Ruth or Frank Zappa? Michael Phelps is also from here. He might be more recognized internationally. Not sure.
I was going to say Morgan Freeman but you win with Elvis (does my being from MS trump LM’s post?).
Also discovered Dana Andrews, Lacy Chabert and Marion Berry are from there too.
Reluctantly I have to agree Clinton trumps Johnny Cash. 
Especially since Hillary has kept them in the public eye after Bill left office.
For Michigan, I’d nominate Madonna; for Hawaii, Barack Obama; Idaho, Sarah Palin.
Barack Obama was born in Hawaii? Are you sure about that? 
Okay, then here’s a few states that haven’t been mentioned yet:
Hawaii: Barack Obama
South Carolina: Andrew Jackson
West Virginia: Chuck Yeager
New Mexico is a tough one. Possibilities include Jeff Bezos, John Denver, Geronimo, Neil Patrick Harris, Ronnie Lott, Bill Mauldin, Demi Moore, and Al Unser - but nobody who seems to really stand out above the others.
For former US territories, John McCain for the Panama Canal Zone.
Alaska is tough, since almost everyone famous from there was born someone else. Probably the most famous native is baseball pitcher Curt Schilling.
I’d be willing to bet that worldwide, more people would know Michael Jordan than would know Franklin Roosevelt.
I’m thinking no. Roosevelt was not only an American President, he was also one of the major figures in World War II.
That’s great for people who know about history. But let’s face it: most people don’t.
Oklahoma has a lot, surprisingly. I’ll post the ones that come to mind and ya’ll can decide who’s most famous:
Garth Brooks (still lives here)
Reba McEntire
Ron Howard (born here, moved age 4 years)
James Garner
Ralph Ellison
Woody Guthrie
Mickey Mantle
Brad Pitt (born here, didn’t stay long)
Tony Randall
Oral Roberts
Will Rogers (my vote for “most famous” but maybe that’s 'cause I live here)
Carrie Underwood
Texas has Dwight Eisenhower. Sadly, we also have Lyndon Johnson.
We also have Farrah Fawcett, Janis Joplin and Buddy Holly. Sadly, we also have Willy Nelson.
Also Howard Hughes.
Worldwide, most people don’t follow basketball either. So I’d take the bet that it would be FDR.
Also Georgia O’Keeffe and Laura Ingalls Wilder.