Let's see...
I've met the bands All-4-One, Boyz II Men, and Night Ranger in the course of my job as a truck stop waitress. When I was a medical assistant, a former Portland police officer who does commentary on shows like COPS and World's Wildest Police Videos (I can't name names for confidentiality reasons) saw the doctor I worked for. I've delivered stuff to a member of the Portland Trail Blazers and he gave me a $40 tip. I met webcomic artists R.K. Milholland (Something Positive) and Aeire (Queen of Wands) at Japantown Anime Faire three years ago and got some really lovely sketches from them.
I've met and talked at length with two of my state's governors, both state senators, and a state representative while serving on my college's student government.
I've also had very nice email conversations with singer Lisa Loeb, and authors David Brin and Anne McCaffrey.
About 4 years ago, my parents ran into Rudy Giuliani while visiting NYC for my cousin's wedding. It was really funny, my cousin's wife had wanted to meet him for a really long time, but of course SHE had to work that day, so everyone EXCEPT her got to meet Rudy. She was so bummed!