Most of the famous people I’ve met are/were country singers. Most of these encounters happened when I was quite small and was dragged along with my parents to concerts and vacations in Tennessee and things like that. So it was always a quick handshake and/or autograph after a show or something. Off the top of my head, I’ve met: Little Jimmy Dickens (I loved him because I was about eight years old and he wasn’t much taller than me), Minnie Pearl, Chet Atkins, Bill Anderson, Charlie Daniels, Hal Ketchum, Marty Stuart, Aaron Tippin (I had a dragon painted on my cheek and he said he liked it and that I was cute. :D), Garth Brooks, Reba McEntire, Martina McBride, Clint Black, Brooks & Dunn…
More quick handshakes and “Hi, how ya doin’? Nice t’meecha” type things, with actors: Robert Duncan McNeill (at a convention, stfu), Jimmy Fallon (at a Thruway rest stop), John Stamos and Rebecca Romijn (in a Walmart).
All the actual one-on-one conversation sort of meetings I’ve had with famous people were authors/editors, and all of the sci-fi/fantasy set. Gardner Dozois, Spider Robinson, China Mieville, Terry Pratchett, Neil Gaiman, George R.R. Martin. And while I’ve not met her face-to-face, I’ve had… conversations… with Anne Rice. And Poppy Z. Brite, as well. That went quite a bit better.
The only ones I really count out of all of these are PTerry, Mr. Gaiman, GRRM and PZB, as they’re the only ones I talked to long enough or frequently enough to possibly be remembered.
I don’t ask for pictures, and I only ask for autographs if I’m actually at a signing or something. I’m always worried about being an Annoying Fan (with capital letters and everything!).