Vandenberg Air Force Base is located just north of the California Bight - the point where the California coast turns from a north-south course to an east-west course. The Chumash, the native people of the region, considered Point Conception and the surrounding area to be the gateway to the afterlife*. When Camp Cook was established in the first half of the 20th century, and later expanded as Vandenberg air Force Base, this upset members of the Chumash community still present in Santa Barbara County. To make matters worse, when the Air Force built Space Launch Complex 6 (SLC-6, AKA "slick" 6) during the 1960s, it is said that the construction disturbed an archaeological site containing human remains. Whether due to the disturbance of the human remains, or the actions of a shaman, the site became cursed (or did it...be sure to read the commentary below).
The project became embroiled in political problems and government blunders. The SLC was originally developed for the Manned Orbiting Laboratory, but this project was shut down after construction. The SLC was then to be the site of space shuttle launches, but these were cancelled after the Challenger exploded in 1986 (an event that some people lay at the feet of the curse). Several rocket launches were attempted, and all failed.
The construction of the complex was also not without problems - bad welds, exhaust ducts trapping gases, extremely bad winds (which, in truth, is normal for this area), and cost over-runs all plagued the project.
Finally, the contractor running the facility on behalf of the air force contacted a shaman, who performed a ceremony to lift the curse. Ever since then, the facility has run smoothly.
Commentary: Okay, alot going on here. Let's start with the "dry facts" and then get into the interesting stuff. First off, this is a classic "built on an Indian burial ground" story. In this case, as in most other such stories, there was in fact no archaeological site at the location of SLC-6, and therefore no burials.
Also, the initiation and cancellation of programs related to SLC-6 makes perfect sense in the context of the nature of and changes to military spending throughout the 1960s and 1970s, so you don't really need a curse to explain that. Likewise, the construction problems are rather typical of the sub-rate contractors who sometimes manage to wrangle their way onto military bases, as well as unique elements of the weather and environment on the base that make construction difficult to begin with.
In other words, you don't need a curse to explain what happened.
Which leads to an interesting question - why did the story of the curse arise to begin with, and why does it persist?
In order to understand that, you have to understand when the story originated. And that would be the 1970's.
As Dwayne Day points out, the story began in the 1970's, during a time of social change and ethnic empowerment movements. The Native American movement resulted in the organization of tribes into politically vocal (and eventually effective) groups that began to protest the treatment of Native American archaeological sites as well as the mis-treatment of Native American individuals and groups. In the midst of this, the development of Point Conception became a hotspot for protests, and, to a lesser degree, so did the development of southern Vandenberg.
Day argues that the curse story began as a way to place blame for the problems at the expensive complex. There may be some validity to this argument, but I think that the explanation may be simpler. The stories probably began as jokes, engineers talking about how the place was "cursed". But regardless of how they started, the stories probably spread for two reasons: A) everyone loves a good spook story, and will tend to share it whenever possible, and B) alot of people hold to the, frankly racist, belief that Native American sites are filled with, for lack of a better term "bad mojo" - which is why the old "built on an Indian burial ground" trope gets tossed around whenever weird things happen at a particular location.
Regardless, the story annoys and offends many of the local Chumash (although I have met a few who think that its funny). This is understandable - how would the average baptist feel if they heard that a place was haunted because their church's pastor had cursed it? Also, beliefs such as this reinforce the "mystical red man" stereotype that has, unfortunately, helped to keep many racist beliefs about the native peoples of the Americas alive.
For this reason, when the contractor hired a shaman to "lift" the curse, this upset the locals, and resulted in the Air Force brass having to do some fast work to try to mend the damage to an improving relationship with the Chumash community.
Wackiness: When I was an intern in the environmental conservation office at Vandenberg, we had, in our library, a paper that had been written by a student at the local community college about the curse. The paper, filled with all manner of hokey pseudo-intellectual silliness, demonstrated that the author was overly-reliant on spell check - the paper constantly made reference to "viscous underworld beings."
So, if the site is cursed, it's okay, the underworld beings who haunt it move reeeeeaaaaalllllll slow, so you can make your getaway without breaking a sweat.
Sources: Personal Accounts, Local Folklore, Internet, Internet, Internet
*Or so it is typically believed, the truth is a little messier, and there are alot of different stories concerning the afterlife and how to get there. The Chumash were not a single monolithic group, but were comprised of numerous different autonomous villages who all shared a language family and material culture. There were probably alot of different beliefs concerning the afterlife, and the confusion regarding whether or not Point Conception was important to it probably comes from the conflation of alot of different stories from alot of different groups.