If you were close enough to see the person with the unaided human eye (I’m going to discount telescopes and binoculers here), share that fact with the rest of us! Here’s my list of celebrity sightings:
Bill Clinton
James Taylor
Bill Maher
George Carlin
Steven Hawking
The only famous person I have ever had the pleasure of meeting was one of the Proclaimers. We met while we were standing at adjacent urinals in one of Edinburghs’ finest public houses nearly 4 years ago.
And, no I didn’t ask him how far he had to walk home. (500 miles I suppose.)
Shook hands with Richard Nixon.
Talked with Michael Hedges.
Got a hug from Elizabeth Montgomery.
I’ve met and had my picture taken with:
Robert Guillaume
Willie Tyler AND Lester
I’ve also moshed with Sebastian Bach at a Motorhead show.
And once, GE Smith was ahead of me on line at the library. I found out later it was because he was performing there, but I didn’t actually see the performance.
Franco Harris (he did a signing at the local mall back the first time the Steelers were winning Superbowls)
Liza Minnelli (went to a benefit concert in Baltimore…met her at the stage door)
Christine Baranski (saw the Kennedy Center production of Mame a couple of years ago)
Harriet Sansom Harris (also the KC Mame)
The Beach Boys
Tommy James
Chubby Checker
The Crystals
Leslie Gore
Davey Jones
Little Anthony
The Grassroots (all of the above singers/bands were at a series of oldies concerts)
Duran Duran (concert at the Tower Theater about four years ago)
Jimmy Carter (whistlestop tour during the 1980 campaign)
Dolly Parton (concert in Hershey last year)
George H. W. Bush shook my hand and talked to me for a bit. He’s much, MUCH more charismatic in person. And extremely tall.
Strom Thurmond used to come to my dad’s company’s box at Clemson home games all the time and drink the free booze. He always called me “sugar”.
I met Gwendolyn Brooks at a book signing and speaking thing at undergrad.
Ditto Stephen Jay Gould.
I won’t count concerts and stuff - it shouldn’t count unless you spoke to them, shook their hand, or saw them at a party or something. 
I thought about that, but it wasn’t specified in the OP so I figured they counted by the rules presented.
I saw Bob Hope in an airport when I was young.
I shook hands with and had a photo taken with David Bowie during his last tour.
Jimmy Carter and Lester Maddox (Maddox is more infamous) (Georgia Governors)
Cris Collinsworth (2x), Boomer Esaison, Corey Dillon (Cincinnati Bengals)
Drew Carey (Comedian)
Elliot Gould (Actor)
Richard Belzer (Actor/Comedian)
Jay Leno (Comedian)
Tom Flores (Raiders and Seahawks Head Coach)
Ron Jeremy (Porn actor)
Paul O’Neill, Chris Szabo (Cincinnati Reds)
Eric Wynalda, Rob Stone and Scott Garlick (Soccer players / ESPN Soccer announcer)
Monte Kiffin (Bucs Defensive Coordinator)
Wilber Marshall, Eric Swann (NFL Chicago Bears and Arizona Cardinals / Florida Gators)
Charles S Dutton (actor)
Brady Anderson (Orioles baseball)
Clay Buchholz (Red Sox baseball)
I think I missed a few. Met a female pornstar once at a bar, but didn’t recognizer (she told me she did adult work). I didn’t really believe her but Googled at home and found out she was who she said she was. Drawing a total blank on her porn name. Only counting people I spoke with or could have reached out and swatted.
Most of these are sports folks. Mainly, because I tend to recognize or remember them.
Angie Dickinson
Tennesee Williams
F. Lee Bailey
John Mellancamp
Andy Kaufman
Leslie Nielsen
Warren Oates
New York mayor John Lindsay
Not including performers in events I’ve attended.
Jennifer Aniston, Courtney Cox, Katie Holmes, Michael J. Fox, Bill Clinton, Bill Murray, Reese Witherspoon, Stephen Colbert
Hmm, I’ll just say one, and he was an Ass.
Bruce Willis. He stayed at the same tiny FOB I was at in Mosul, Iraq. He was hanging out at the chai bar with his shades on ignoring any and all troops that came to talk to him. A few of us tried to chat him up and he was just a jerk. Uhg. JERK!
Edit:
Ok I’ll add the rest:
Ben Folds (my idol)
Reggie Miller (grabbing a sandwich in town)
Karem Abdul Jabar (at a gas station)
Donny Rumsfield (jack ass)
Oprah (at Ft. Campbell for the worlds largest baby shower)
Cindy Crawford (see above - absolutely gorgeous)
The most famous person that I’ve been reasonably close to (but not actually met) was Bertrand Russell at a Committee of 100 demonstration in London (he would have been about 89 years old, and I was about 16 years old – it was my first demonstration).
Peter Yarrow - Had dinner at his house
John Kerry - Saw him shaking hands outside my house in NY during the campaign on St. Marks Place
Sarah Michelle Gellar - She was eating at the Italian place by my house in Little Italy
Timothy Hutton - Used to hang out with him
Kevin Bacon, Gwyneth Paltrow, Harvey Keitel and many others - passed on the street
Marilyn Manson and his band - Was signing autographs at Virgin when I went to a screening of some film I forget which
Governor David Paterson - Met him when I did sound for an event he spoke at when he was a Senator
Neal Stephenson - Met at a book signing
Scarlett Johanssen - Met her at a screening for a short where her brother Adrian played someone loosely based on me. She was like 16 at the time, it was right after the Horse Whisperer.
Joey Ramone - He was at Coney Island High on St. Marks once
Peter Steele - He used to go to a club I went to.
En Esch from KMFDM - He used to go to clubs I went to
Rudy Giuliani - Gave a speech right below my window in Little Italy
That’s all I can think of. Living in New York you see celebrities all the time and there are certainly more.
Gregory Peck
Cecilia Peck
Lauren Bacall - I was an extra in a movie with the three of them when they made a film in Raleigh. They used our movie theater to run their dailies and I saw them every night for at least a month.
Have my picture made with:
Carlos Mencia
James Denton (Mike on Desperate Housewives)
Several NHL (or former NHL) players:
Glen Wesley - he’s a good friend of my boss and I’ve driven his car and been to his house
Rod Brind’Amour
Cam Ward
John Grahame
Michael Leighton
Scott Walker
Ray Whitney
Eric Staal
Sergei Samsonov
Frank Kaberle
Mike Zigamanis
Amazing Johnathan
Carrot Top
Dave Attell
I’ll be able to add Terry Fator in May.
I know there are more, but I’m not remembering them right now. I’m not counting concerts and shows where I just saw them on stage.
I yelled “Hey Evil” at Evil Knievel from a passing van when I was a little kid.
A couple friends and I saw Michelle Pheifer at the Dekalb Corn Fest about 10 years ago when she was in the area filming a movie. She was taking her kids on some rides and we just happened to take my friend’s daughter on the same rides.
I met a former NFL lineman once in Vegas. I honestly don’t remember who it was, so I guess he wasn’t that famous.
If we stick to people I’ve seen UP CLOSE…
The Dixie Chicks (they used to play trivia games regularly at a local Irish bar I frequented. I sat close to them several times by chance, but never talked to them. They were usually with friends and family, and I could never think of any good reason to bother them.)
“Jungle Jack” Hanna
Chuck Jones
Ted Koppell
Bob Lilly
Ann Richards
Tommy Smothers
Cheryl Tiegs
Tom Wolfe
Oh, and of course, Regis Philbin, whom I met for about 5 seconds during my taping of “Who Wants to Be a Millionaire”
(I never made it to the Hot Seat, and didn’t win a cent.)
Just going with some of the high points here:
Buckminster Fuller (giving a speech, about a year before his death)
Stephen Hawking (speech and reception)
Chuck Yeager (speech at the Smithsonian, 50th anniversary of first supersonic flight)
Bill Clinton (speech and handshake line during '96 campaign)
Roger Ebert (speech, Q&A, and booksigning)
Simon and Garfunkel (concert during their '82-'83 tour)
John Lithgow (singing and reading one of his children’s books)
Mitt Romney (two rows ahead of me on an airplane, while he was governor)
Bob Gainey
quite a few, special mention for Thom Yorke who was a complete douche.