Can an American and a Canadian get married in the United States without a fiancee visa?

Nope. Jump through the hoops and get that Fiancee visa. It is easier, and cheaper to get a Fiance visa to enter the US than to get married and apply for a permanent residence as a spouse of a US citizen.

Answer

Sorry to disagree with upstairs answer but the answer is - YES! I am assumimg your ALREADY in the USA. In that case you can get married and then you can file for permanent residency as being married to a US Citizen like I did!

umm... YES!!!! loveyyDoveyss can f*** each other in the USA too!!!

^^^^^^^^Are you sure about that? And how did you get your belongings from Canada into the US??