UPDATED with Charlotte Rampling (thanks to a reader for noticing my omission).
These four birthday girls are responsible for a lot of screen nudity.
Laura Linney (55 today, at least seven nude appearances) in Maze (2000)
Jennifer Jason Leigh (57 today, about 20 nude appearances) in Fast Times at Ridgemont High (1982)
Barbara Hershey (71 today, at least eight nude appearances) in The Entity (1981)
Charlotte Rampling (73 today, about two dozen nude appearances) in The Night Porter (1974)
While Laura Linney didn’t appear in as many scenes as the others, her record is still impressive when you consider that she never did a nude scene until she was 35 years old! Rampling didn’t get started until she was 27 (in The Night Porter, see above), but quickly made up for lost time. The other two were youngsters when they started getting nekkid on screen: JJL was 19 when Fast Times (clip above) was filmed; Barbara Hershey was 20 in Last Summer.
The Entity, linked above, includes a mixture of Hershey’s body and various elements of movie magic like prosthetics and a body double.