I'm in a discussion about this. To me, since this is an electronic mail, it should be check your email, but the client insists on check your mail. My rationale is that email is for... well, emails, while mail is associated to physical mailing delivered by courier and post offices.
However, since English is not my native language ( not even the second), there's a chance I'm totally off. Besides, he's from US (hence English is his native language) and quite honestly, whether it's labeled as email or mail, I can't even imagine what to put in that field if not an email address, so at some point, the discussion seems quite abstract to me.
On top of this, does this change of words have an influence on usability? I mean, is "enter your mail" any different than "enter your email"? Or do users understand the same thing? And what about email vs e-mail?