The first successful launch of SpaceX was the fourth launch of Falcon 1 on Sunday 28 September 2008. The first three failed due to a variety of design problems. In a later interview Elon would tell, that if the fourth launch of Falcon-1 would have failed it would pretty much have meant the end of SpaceX because he was running out money and with no successful launch vehicle nobody would buy a payload ticket. Luckily the fourth launch went picture perfect and SpaceX is now a thriving launch provider for both commercial satellites and SpaceX own Dragon capsule.
SpaceX is very busy making huge progress. Three future milestones will be demonstrations flights from Vandenberg Air Force Base, to qualify for military satellite launches, which gives SpaceX access to a very profitable market that will fund and speedup all over development. The second one will be the qualification of Dragon for manned missions to the International Space Station. The third will be the first vertical landing of the first Falcon-9 stage. At that point SpaceX will be the fist company that can reuse the biggest and most costly part of there rocket, which will bring down launch prices dramatically.
A lot has happened since that first successful Falcon-1 launch. A lot will happen in the near future. Enjoy the video, it has some great footage about not only the launch, but also about the inner workings of the Falcon-1 and a nice ad hoc speech of Elon himself.