Last Saturday, on March 27th, 2004, NASA's Supersonic Combustion Ramjet (the X-43) broke all known airspeed records, reaching over 5,000 mph at an altitude of nearly 100,000 feet. Here's a Space.com story that gives some of the interesting details. This successful trial was the first known hypersonic flight (not counting glides, such as the Space Shuttle's re-entry) and represents an important milestone towards cheaper and more efficient space travel.
A scramjet is far more efficient than a rocket or a conventional turbojet because it "breathes" air and has far fewer moving parts -- in fact, many scramjet designs have no major moving parts, consisting of little more than a compression chamber, a fuel injector, and an exhaust vent.
The trick is that in order for the scramjet (or it's cousin, the ramjet) to ignite, the vehicle carrying it needs to be moving fast enough to compress the air in the compression chamber so it can be mixed with fuel and combusted, and this critical pressure requires supersonic speeds; a scramjet-propelled vehicle needs some other engine system to boost it to Mach 1, and generally a rocket is used and discarded once its fuel is spent.
Update:
Carl the aerospace engineer has more on the X-43A and engines in general. He says I've got misconceptions, but I don't think I wrote anything that contradicts his more detailed and knowledgable explanation.
I'm an aerospace engineering graduate student and I have a post on my blog about the X-43 and hypersonics. The main thrust of which is that the propulsion system most efficient changes depending on how fast you want to go. The scramjet is best for very high speeds, but inappropriate for mere supersonic flight. Check it out at http://antidisestablishmentarianismesque.blogspot.com/
Nice post with more explanations, but what were my misconceptions? :)