Robert Bigelow, owner of Bigelow Aerospace, has set up the America's Space Prize with a 50 million dollar purse up for grabs. Way up. Check out this article about the rules. Also look at this more general article.
This contest makes the X Prize look like stretching before a marathon. The challenges involved are considerable. I recall Burt Rutan (winner of the X Prize with his SpaceShipOne) making a statement about wanting to go orbital, but I don't see any way to scale up his current design to fit the task. It would be like "scaling up" the Space Shuttle to go to Mars.
First of all, the altitude to beat is 400km, while the International Space Station orbits at 360km. Secondly, it has to be able to dock with Bigelow's orbital habitats, which is no small trick. In addition to the maneuvering hardware and an airlock, it will necessitate an orbital velocity similar to the ISS, which currently averages 27,685km/h. If you can do that, the other requirement of achieving at least two orbits will be no problem.
Of course, much like mountaineering, "a successful ascent not only involves reaching the top but also includes returning to the bottom." Deobriting from a 400km, 27,000km/h orbit is a significant challenge all by itself. That is after all, what destroyed the Space Shuttle Columbia.
Because the vessel has to be reusable, it seems to me that there would be about three basic concepts that could potentially pull this off. The first would be the plan pursued by JP Aerospace, which involves using two stages of airships to reach orbit. It would be a slow trip, but potentially quite safe.
The second would be to use two rocket propelled stages. A reusable, glide-able booster stage would get the craft up to say 100-200km or so and the second stage would achieve orbit while the first stage would glide back to earth and land on a runway.
The last concept would be to use a large carrier aircraft to lift a spaceplane with a hybrid ramjet/rocket engine to roughly 40,000 feet. They would then separate and the spaceplane would reach orbit. I'd say this is the least likely of the three as ramjets are still experimental.
The reality is that it is highly improbable that anyone will claim this prize by the Jan. 10, 2010 cut-off date and I expect many to come out saying that it is impossible to win. Of course, never forget the two best reasons men have for doing anything: "Because I can" and "Because you said I couldn't."