Lulu, yes. Like any living thing, they can become extinct. Smallpox is extinct in the living population, though it exists as a bilogical weapon (allegedly, though it's almost certainly true).

When you get measles, while you have the disease it is multiplying like crazy in you and getting out via liquid droplets (in sneezes, coughs and your breath) to other people. If they inhale it and are not immune (through vaccination or previous exposure) they get infected. However, your body launches an attack on the measles cells and kills them all, and you get better. If enough people are vaccinated that there is no-one for your measles to infect then it dies out.

Polio is on the verge of eradication right now, which is tremendously fantastic news.

Bx