I've had a few. Saw Jude Law, Sadie Frost, and Kate Moss (all together, obviously pre Law/Frost divorce) at a Radiohead concert in Oxford. I was really obsessed with him at the time so it was a big deal.
Sat very close to Luke Wilson in a restaurant... and stared a lot
Billy Corgan offered to phone my mother to ask if we could go to a Smashing Pumpkin's concert. It was at an autograph signing with my sister, and when he asked if we were going to the concert the next day, we told him we weren't allowed. He said he would give us free tickets if our parent's would let us come. I could only reach my father who made the offer "If he comes to church on Sunday morning, you can go to the concert Sunday night" I just hung up the phone.
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Most recently.. we flew back to London this Tuesday and Karl Rove and Donna Brazile were both on our flight from Atlanta to Heathrow. We were sitting in the back of an empty lounge across from our boarding lounge, and they came and sat very close to us. It was a bit surreal as CNN was on and talking about all the bad policies of the Bush administration. I heard Donna on the phone saying they were travelling to Africa.