So they do unit and integration tests? Sounds thorough...
The engines on your 777 are designed so that a 6ft long fan blade moving faster than the speed of sound can break off and not go through the engine cowling and into your lap. They blow up $30M engines in testing to prove this
I think that's a very good way to put it: nasa gets rockets built so they work, all of their engineering is built so it's as perfect as can be from the start. It's a huge cost, but it allows them not to blow up rockets in testing. SpaceX sees that as spaceworthy aircraft-building, they drive up-front costs lower by not focusing as much on design reliability and instead blow up engine to test how they behave.
I'm saying that pragmatically, unrecoverable errors don't need testing, and NASA's class of possible unrecoverable errors is much wider than any airline's. The fact that SpaceX feels the need to test so rigorously is a good sign about what they want to be "recoverable" and therefore about how safe their hardware is intended to be.
Engines can fail in many ways that don't destroy everything. Apollo 13 nearly became famous for exploding on launch due to massive resonant vibration, but a premature shutdown of the affected engine saved it. (Oddly, that shutdown was due to a mistaken fuel level reading, not the vibrations directly, so the save was something of an accident.) At least one Shuttle launch experienced an engine failure/shutdown as well. These engines didn't explode, of course, but there's a whole range of failures and many can be planned for.
Even when the entire thing does explode, you can still save your crew if you've planned properly. A Soyuz capsule's escape system saved its crew when the rocket exploded in 1983.
It appears to me that NASA's approach is to prefer systems which can't fail over systems which can fail safely. On the surface, this seems better, but when your foolproof system still fails and you haven't built it to withstand that, then you're in serious trouble.
I don't think there's any inherent reason why shedding a turbine blade during a rocket launch has to destroy the entire vehicle. Designing the system to withstand that makes it heavier and not perform as well, of course, but it seems like an overemphasis on performance while disregarding nearly everything else has really hurt space technology.
There's a video of the Soyuz explosion mentioned above at http://www.youtube.com/watch?v=UyFF4cpMVag&noredirect=1 that shows the escape system saving the crew.
The use of solid rocket boosters for human space flight (as was planned for Ares I) is hugely controversial because they can't just be shut down in the event of a problem, as regular engines can, making survivability more difficult.
Personally, I think NASA is overly risk-adverse, to the point that nothing gets accomplished (see Constellation / Ares I). An interesting article on this is http://www.popularmechanics.com/science/space/news/4330356
On the topic of aircraft turbine failures, there's the interesting case of a DC-10 engine that disintegrated in flight due to a pilot experiment, killing a passenger. For details see: http://en.wikipedia.org/wiki/National_Airlines_Flight_27
Finally, if you're interested in SpaceX, NASA budgeting, and so forth, I recommend http://nasawatch.com
In the Challenger accident the engineers estimated the chance of a fatal accident at 1:100 , the next level of management 1:1000 senior management at 1:10,000 and the official Nasa press release 1:300,000
Presumably by adding more levels of management they could have made it even safer!