I think most of the answers so far are speaking about the use of the terms in the US.
In the UK, it's always called a CV, with the exception of a few specialist fields like performance arts, musical theatre, acting, etc., where it is called a résumé (and this will not necessarily Résumé would be known by people outside those industries).
These fields exceptedunderstood, I always assumed résumé was just the Americanbut it's a US English term for CV. The assertion above that CVs are some monstrosity of "an untold number of pages" is just not true here. Standard CVs are almost ubiquitously two pages long (although, although academic ones may indeed be longer, and ones in other particular fields may be shorter).
In short: CV is the dominant term for the document, but there are a few special circumstances where you might say résumé instead.