Can a Canadian citizen live in the US if he or she marries a US citizen?

Yes. When a non-citizen marries a U.S. citizen, s/he can then apply for US permanent residency. It is important to note that you cannot marry someone solely to obtain a green card as that is considered fraud (though, for the most part, it is the government's burden to show fraud, not your burden to show it isn't).

A Canadian citizen married to a US citizen should have a simple time getting the required permanent residency visa, though you still must fill out the proper immigration forms and follow the rules to the letter, as NOTHING is automatic.