Hi Sara!
According to wiki the US introduced them in 1943, Germany did in 1941 and the UK might have been using them since the early 20th century.
They´re used by 117 nations as of 2003, including Europe (except Irland, but they want to, too).
Switzerland: 1964, 4-digit codes. There is also a wiki article on them, including spefic postal codees. I´ll link it when I get home
Hope this helps, Michael
EDIT: no with link:
ZIP Codes in Wikipedia