I've read through quite a few of these entries, but at 51 pages, it's a bit much! However, figured I'd add my two cents . . .
I would never approach or even acknowledge a celebrity who is eating / shopping, etc. I just think it's rude and tacky, and autograph seeking I find rather odd as well, but I know many people like to get them.
Cindy Crawford - was at a bar with her in her hometown in Illinois, we did shots and chatted, she was fun (this was in her Richard Gere days)
Billy Corgan (lead singer of Smashing Pumpkins) - I ran into him by chance when they only had one album, they were opening for Red Hot Chili Peppers in their heyday. Billy and chatted for a very long time and he gave me a backstage pass on the spot, asked me to hang out later in the evening
Eddie Vedder and Jeff Ament (Pearl Jam) - Also met by chance when I made them laugh and they called me over. Lovely men. They were about to release the album Ten and I still remember telling them I had never heard of their band - was shocked to see them on MTV a few months later!
Black Crowes - I am not shy, but suddenly became shy backstage at an Aerosmith concert as my friends passes were not located so I was alone. They came over and sat down with me saying I looked frightened. I was so glad they did that!
Noel Gallagher - I ran into him at a members club a few years ago, didn't recognize him straight away and he was friendly to me as we chatted a few minutes - I turned to leave and saw my friends just standing there with their mouths agape, then I realized who it was!
Bob Costas - major sports presenter in America, we shared seats on a long haul flight (the only time I've sat in first class!). Really nice man, talked just the right amount for a flight.
A good friend who shoots music videos says the two most difficult stars she's worked with have been Mariah Carey and J-Lo. She says Mariah is demanding and just weird (no surprises there) and J-Lo has a no eye contact rule from crew. She said the eye contact thing is impossible as she is doing the filming so she needs to be able to look straight at J-Lo, but this apparently infuriates her.
I've got more but this post is getting way too long!