Acting: the importance of (not)having an accent.?

[Vault Dweller]

I have an accent that sounds very pleasant (at least that's what many women tell me)...I would not attribute it to a particular geographical area...it's probably a mixture of accents...or just my own accent...many of my words sound kinda British......ANYWAY, HYPOTHETICALLY, IF I WERE TO PURSUE AN ACTING CAREER SOMEWHERE IN NORTH AMERICA (both Canada and the US in either theatre or movies) would it be a good idea to lose my accent (and start speaking with an american accent instead)? Can you get a role in a Hollywood movie (don't laugh - it's a hypothetical situation) if you have an accent that is not American? Is, overall, a non-American accent a huge obstacle when it comes to acting in North America?
long descriptive answers from people familiar with the acting world would be interesting to hear (although I'm interested to hear all answers)