Why Not Hydrogen-Fueled Planes?

I was pondering this idea the other day: as we see the price of oil skyrocket and dream of a hydrogen economy, why do we hear so much about implementing hydrogen as a fuel for automobiles and not as a fuel for planes? Given the infrastructure challenges facing hydrogen-powered cars, it would seem to me to make more since to roll out hydrogen-fueled airplanes, instead. There are fewer airports than there are gas stations, the refueling of planes is accomplished by more trained workers (a concern for self-serve hydrogen fueling stations), and switching to hydrogen-powered planes would significantly reduce our demand for oil. Yet, I haven't heard of any planes that run on hydrogen. An Internet search for hydrogen-powered airplanes turned up lots of environmentalist websites, no mainstream media sites, and a couple of research articles. Boeing, according to the one article that I read, seems to doubt the ability of hydrogen fuel cells to be the primary source of power for commercial aircraft. Whether this inability truly exists, or whether it's more of a "640K out to be enough for anybody" statement, remains to be seen. I'm all for switching to hydrogen power overall. So, to all mechanical and aerospace engineers out there, no nay-saying about this idea. Let's get those fuel cells and/or hydrogen engines functioning at a high enough level that we can drop oil as our main fuel source.