Project Orion

Way back in 1947, a rocket was designed that would be able to accelerate as fast as 80% of light speed, and worked better with larger masses (thus making space travel freakishly cheap) and would cost about the same as the smaller rockets we now favor. It was called Project Orion, and was only scrapped because of nuclear paranoia. For you see, Project Orion's main propulsion was essentially nuclear bombs.
Orion would now be illegal to build under the Partial Test Ban Treaty of 1963, which requires that all nuclear detonations be done in underground bunkers. Detonations in space would be right out, to say nothing of detonations in the open atmosphere. The safest possible launches would have been from the poles, where radiation would not have been magnetically drawn back to the earth.