The British actress was one of Disney's biggest young stars in the 1960s, winning acclaim for her roles in The Parent Trap and Pollyanna.
Mills was bombarded with fan mail from around the world, including lavish gifts - but one devotee left her parents uncomfortable after asking the teen for her hand in marriage.
She tells Britain's Daily Telegraph, "The only sense I got of my fame was the fan mail. There was a lot, mostly from people my age, and my parents were adamant that I replied to every letter. Often it was just signing a picture, but if I received a particularly nice letter or a present then I had to reply with a letter.
"I got some remarkable presents. Someone in Africa once sent me a monkey rug, and I was sent a diamond ring, which I was thrilled about, but it came with a proposal for marriage, so I was made to send it back."