Crikey, where to start.
Fortunately in my line of work (building maintenance) we have to ensure that everything works when anything celeb related takes place, as such I've met absolutely boatloads of them, and living and working in London really helps with this too.
I've met Daniel Craig when he was filming Casino Royale, he filmed a scene at Moorgate (Aldermanbury to be exact), this was my first experience with this kind of thing so naturally I was extremely excited to tell everyone that "I was there! I was there!" only for it to be like two seconds in a chase scene in the film.
I met Dustan Hoffman and Emma Thompson when they were filming Last Chance Harvey, they did a scene at the book market on South Bank, I was looking after the BFI at the time so chatted to them for a bit (this was where I learned that actually these people were just being polite to the young exciteable kid and actually didn't actually have time to talk to me, as their usher soon told me, another lesson learnt)
I've met all three of the Top Gear presenters, Clarkson in the middle of his "slope" controversy, he was outside his lawyers and properly grumpy when I greeted him, he still remained polite and said it wasn't a good time, fair play. Hammond I met on a chance visit to Saunsburys in Fulham Wharf. Just a quick hi, nice to see you, thanks for all the entertainment kind of thing. May I met at Waterstones Piccadilly when he was doing a book signing and we had to sort out all his back-of-house stuff.
During that same employment I met loads of other minor celebs, Stephen Fry, Katie Price, Sean Lock (

), Jimmy Carr and probably loads more I'm forgetting.
I've met Hugh Grant loads of times, he has a house next to my former billionaire employer's house in Kensington and his mum used to park at my boss's place and I'd often have to ring them up to get them to move their cars. Genuinely nice chap tbh.
I've met JK Rowling when she was living on Eaton Square and I had to replace her taps, same with Naomi Campbell. Met a few other famous faces during that time but can't remember them all.
More recently I've met Sir David Attenborough when he came to open the new Fixing our Broken Planet exhibit here at the Natural History Museum. I've also met Tom Cruise who was filming the next Mission Impossible, also here at the museum. Hoping there's more than two seconds in the film this time! (also had to fire one of my staff for breaking the very strict no-cameras rules unfortunately).
I've met tons of people from the Royal Family too, as they are huge supporters of the trust here at the museum and often pop in to see new exhibits and stuff. Never the big ones, just the little namby pamby ones.
I've also met tons of celebs from other countries, mostly arabs and sheikhs as London is their playground and a couple of years ago the museum was the venue du joure for their events.
That's all I can remember off the top of my head, I'm rather fortunate like that. Pity it's all wasted on me, celebrities do absolutely nothing for me. Glorified jesters. Dance puppet, dance.