Oooh - this got me hooked for a good half-hour. It would appear that "Cheers as a salute or toast when taking a drink is British, 1919.". Opinion seems to be divided as to whether it's a contraction of "Good Cheer" or "Three Cheers" (as in 'Hip Hip Hooray' - a possible origin also of the British salutation "Pip Pip", used around the same time - see any PG Wodehouse :) )

Nowadays, I'd say it's probably one of the most commonly-used words in the UK, used for 'Thank you' and 'Goodbye' as well as being the 'standard' toast - I've even heard old guys in the pub mutter it to themselves before starting to sup their pint.

Chin chin,
Ben