High school or college.
Ever.
If you have more than one, it’s fine to list them, just make the Most Famous one the first on the list.
And do please name the institution. 
I don’t know if she graduated from my high school, but I know Kristen Johnson (Sally from 3rd Rock) went to my high school. Between my High School and College, I’d call her (arguably) the most famous.
The University of Illinois–Hef.
High school: Baseball player Jim Thome
College: Either Ray LaHood, the current Secretary of Transportation, or Neil Flynn, the guy who played The Janitor on Scrubs.
Kary Mullis, the controversial Nobel Prize winning scientist, went to my high school.
Katherine Harris, the Florida Secretary of State for the 2000 election fiasco, went to my college (Agnes Scott) - I was there at the time and reporters kept trying to get her yearbook from the library. I suppose she’s the most famous graduate I can think of.
Supposedly Joe Kennedy and Tom Menino graduated from UMass-Boston. (I’m not finished yet)
I’d say Burt Reynolds or Deion Sanders from Florida State University. Jim Morrison attended the school as well.
High School - Star Jones. Sad.
College - anyone who graduated from Georgia Tech.
Joe
Lou Piniella
High School
Nobody famous from my high school.
NC State - John Edwards
High School: Robert Altman
College: Regis? Nicholas Sparks? Joe Montana?
Gary Larson, Edward R Murrow and Keith Jackson
College - I went to West Point, so it’s highly debatable. Probably Eisenhower or Grant are the most famous.
University of North Carolina at Chapel Hill
James K. Polk (11the US President, class of 1818)
Thomas Wolfe (novelist, class of 1920)
Shelby Foote (historian, attended 1935-37, did not graduate)
C. Vann Woodward (historian, PhD 1937)
Charles Kuralt (journalist, class of 1955)
Michael Jordan
A Cy Young winner graduated from my high school.
A bunch of famous people graduated from my undergraduate school.
I was going to say Roger Ebert.
Aaaaaaaaaaand, later it occurred to me to check on my grad school, and Emmylou Harris’ name was the most noteworthy I saw.
Just checked my grad school as well:
Mark Cuban
Isiah Thomas
Mark Spitz
Coolest: Will Shortz, NYT crossword puzzle editor
It’s hard to say who is the “most famous” - there are a lot of different ways to be famous.
Here’s some famous graduates of Ole Miss:
Writers
William Faulkner
John Grisham
Actors
Cynthia Geary
Gerald McRaney
Sports
Archie Manning
Eli Manning
Deuce McAllister
Politics
Jamie Whitten, second-longest serving U.S. Representative ever (1941-1995)
Trent Lott
Military
Admiral John S. McCain, Sr., USN; grandfather of Senator John McCain
Fictional persons
Dr. Leonard “Bones” MCoy (Star Trek medical officer)
Brian Mulroney, Prime Minister of Canada from 1984 to 1993.
Jean Chrétien, Prime minister of Canada from 1993 to 2003.
There may be others but I limited myself to the two most prominent examples of people who graduated from the same department I did.