Gah. I was just going to post something about Deep Impact. Anyway...
It didn't explode, and nobody expected it to. Believe it or not, the city-sized comet itself was completely unaffected by the blast. Its orbit didn't change a bit, only the inner layer of dust and gas around the comet increased in size. Hubble was pointed at Tempel 1 at the time of the impact, but it didn't get a very clear picture due to the cloud of dust and gas surrounding the comet.
The main reason NASA is doing this is for the reasons people have already stated. They want to see what's at the core of the comet and study it. Comets, asteroids, and other "floating junk" are believed to be the some of the oldest things in our Solar System. If we know how they were formed, we'd know how most other things in our system were formed as well.
There's a Universe Today article about it
here. We're alive for history, this is the first time we've put a probe on something other than a planet (awaits bad probe/Uranus joke).
EDIT: Holy crap, Prozac. I thought you were joking until I looked that story up. o_o
Apparently this whole incident cost her $311 million in moral and spiritual damages? That's funny, because I doubt it even cost Tempel 1 that much damage, and it was the one getting hit by Deep Impact.