I have it on good word that SpaceX successfully tested the engine that powers their rocket, the Falcon 1. They fire the engine with the rocket essentially strapped down so it doesn't launch. This is called a static test or static firing, and it went very smoothly. Unfortunately, no video is available (the image above is from an old test).
SpaceX is a start-up private space launch company helmed by Elon Musk-- one of the cofounders of PayPal. Last year, almost to the very day, they attempted to launch the first Falcon 1 rocket, but the rocket was lost. A corroded nut allowed a fuel leak which doomed the rocket.
However, extensive testing should avoid that and other problems. We can hope! The actual launch of the Falcon 1 rocket is planned to be soon, but no date has yet been released. It'll probably be next week sometime.