I did Christmas Carol first when I was 8 years old, playing Fan. My parents bought me an annotated illustrated version of the book, and I proceeded to have everyone from the production sign the book wherever they liked. Some took the big center illustration of Fezziwig's party. I myself in my 8-year old large handwriting - complete with smiley face dotting the i - signed my own name right by Fan's part. I've continued to have people sign the book for each production I've done. And then I try to read it through again every year.
When I've done musicals, I've also had people sign a book of the sheet music, though not every time. And it really makes those sheet music pages come alive when I pull it out at the piano again years later.
As for doing the show itself, I used to work on a large Christmas touring show for sometimes 100+ performances a year, for 5 years. You still found ways to enjoy the show, whether the bits you'd do behind the scenes (never noticeable by the audience, but to keep the performers happy), the joy of meeting an old friend for the first time every year, the joy of getting to know new people every year. The "knowing what you're getting into" with some people and the new ways to figure things out and improve each year. The fact that the paperwork doesn't have to be started from scratch when you've got a basic premise to start with, etc, etc. It's nice to put the show away at the end of each year, but also nice to know what you're getting into.
And now that I've returned to the world of freelancing for the first time in a long time, I'm enjoying when I see a show on the job listing that I have already done. Goes right into my cover letter with specifics on some moment or feeling about the show, and hopefully puts me closer to the top of the pile.
[And I like PSMKay's comparison to that every-December ritual, too.]
EDIT: Guess I should list some of the multiples I can remember.
Grease -just remembered I did 3 versions if you count the one I was in the orchestra
Guys and Dolls - 2
Anything Goes - 2
Oklahoma - 3 (once in it, once stage managing, once on the marketing team)
Radio City Christmas Spectacular - 5 years touring
My Fair Lady - 2
Music Man - 2
Spent 9 1/2 years working in the education and community department of an opera company, with a rotation of about 10 productions, plus a slew of one-off concerts
Christmas Carol - 3
Erin