The famous Zayak rule (you can only perform 2 of a specific triple jump, and one must be in combination) - this rule was to limit the amount of triples done in a program, since skaters, like Zayak, would do many triple toes in the LP.
There's also what is loosely called the Asada Rule, which is to allow women to perform a solo triple axel in the short program. This replaces the previous double axel requirement, which will now be a double or triple axel requirement.
There was also a loosely termed "Witt Rule" that required ladies to have a skirt as part of the costume. Remember Witt, back in 1988, had the controversial SP costume with the feathers. A rule was imposed for ladies to have skirt material on the costume, but that rule has since been replaced with new costume rules...one of which allows women to wear body suits.
As far as moves:
Biellmann
Axel
Salchow
Hamill Camel
Harding Spin (not really a famous move, but love Dick Button's "cross between a Hamill Camel and a tipsy skater")
Tano Lutz
Rippon Lutz
How many skaters can you name that have won two or more Olympic medals?