It depends so much on the celeb, but usually I tell them a little bit about me and I'll talk about how I got to know their work "I saw you that one movie 10 years ago", then I'll talk about my favorite work of theirs "My favorite movies of yours are..........." (honestly I'll look up on IMDB in case I've forgotten about a movie or two, example I think alot of people have forgotten about how awesome Hugh Jackman was in Swordfish), followed by an autograph request "could you send me an autographed photo, it would mean alot to me", and I say something along the lines of "I know you're very busy, so I want to thank you for your time", then I write, "Thanks for everything, " and sign my name. Usually it's about 2 or 3 paragraphs, but it does depend. If I know my letter will never make it to a celeb and only to a Sec, I'll put less thought into it, if it's a celeb I absolutly love the letter usually longer and more meaningful, and sometimes I throw in a quick joke if I think of something clever

I start off by saying I loved them in whatever movie I liked. Or I say I like their music, etc.
If I'm writing to a guy, I'll tell him he's cute/hot/sexy, etc. I usually write no more than 8-10 sentences.
And I usually handwrite so the letter seems more personal. I end with saying, "can you please sign this photo I sent? I'd really appreciate it and I guarantee I will never sell it". I always send a SASE so they can return easier/faster.

This is just a question because I'm bored and curious.

How do you phrase your request? Do you specifically ask for an autograph or do you just write a fan letter and hope they reply?

I usually write a page or so about how much I like the celeb's work, then I say something like "If you aren't too busy, I would love to receive an autograph. You are one of my favourite actors/actresses/musicians/whatever, and it would really mean a lot to me. Etc."

So, what do you say?