Looking For U.S. Work Visa?

bueller asks: "We hear about the U.S. trying to increase the number of work VISAs available for foreign workers, and the long wait to get VISAs, but how are 'aliens' gaining work in the U.S.? Are certain companies more receptive to supporting non-citizens wanting to work in the U.S.? Are people just turning up and looking for work, or do they have work organised before arrival? I'd like to work in the U.S. for a couple of years, but I'm not sure if I should be applying directly to U.S. companies, applying for the small number of U.S. positions offered through agencies here, or going with companies that specialise in placing people in the US. "