We invited the Obamas and Alex Trebek to our wedding. (Not randomly - I thought maybe I’d get a note or something since I was a contestant, and I’d heard you get a nice card if you invite the president.) Trebek (or more likely an assistant) very cutely filled out our regrets card.
Thanks for the reminder – I’ve corresponded with Lileks semi-regularly over the past decade or so.
I became friends with my favorite celebrity and we talk on a semi-regular basis. 
The dorm floor that I lived on as an undergrad had a tradition of inviting various celebrities to be Guest of Honor at our big yearly shindig. They’d then post the letters declining the honor for everyone to see.
I suspect they’re still doing this – it’s too good a tradition to give up.
I haven’t, but my little sister sent a letter to Terry Pratchett when she was twelve (she wanted more books about Magrat).
He wrote back, told her that there would be a bit of Magrat in his next book.