Dear PoPville – Would we be crazy to use a non licensed contractor?

Photo by PoPville flickr user Néstor Sánchez Cordero

Dear PoPville,

We are getting ready to begin a bathroom renovation followed by a kitchen renovation. I am in the process of getting bids from various contractors, however, we have had a number of contractors recommended by neighbors who are not licensed in DC or bonded. Has anyone had experience in dealing with similarly situated contractors? Would we be fools to use a company that claims to be new to the area and is not licensed in DC?