Background information:
1. Space shuttle's main engines (not the boosters) are hydrogen-powered.
2. There are (experimental) hydrogen-powered cars which actually burn hydrogen instead of gasoline (I'm not talking fuel cells, but hydrogen-based combustion engines!).
Considering that, would it be possible to have jet planes using hydrogen instead of kerosene? Would the re-design costs for the engines be prohibitively high? Would keeping the hydrogen liquid be too expensive at the airports and maybe impossible in the plane tanks? Would it be too dangerous, because of hydrogen's high inflammability?
If not, why is no-one working on that? Why is there development on cleaner cars, but not airplanes?
The main problem of hydrogen is bulk, and second, its cryogenic nature — it need to be chilled to -252 C (-423 F) to be in liquid form.
First, the bulk issue. Liquid hydrogen takes about 4 times the volume of hydrocarbon fuel for the same amount of energy. Since long range airplane have fuel filling all of the wing, replacing jet fuel by hydrogen would mean filling the fulelage as well, leaving no room for the passenger or cargo, unless you are willing to have a much enlarged fuselage, or external tanks. But enlarged fuselage or external tanks would create more drag, so would need more powerfuel engines using more fuel. Hydrogen cars are easier to achieve because a car range is in the order of 300 to 400 km. Long range airplane can go 16000 km (about 9000 miles); and they need proportionally much more fuel than cars; up to half their maximum take off weight can be fuel.
Then you have the issue of the cold. A rocket can get by because it will remain in the atmosphere just a few minutes before reaching orbit — and even then, the insulation of the external tank of the space shuttle has proven problematic as we all know. But a long range airplane can be in the air for 14 hours or more, sometime flying in the rain and snow, imagine how much ice from condensation it would accumulate in the period. So thick insulation would be needed, adding even more to the bulk.
Companies ARE studying hydrogen fueled airplanes, but until a good solution to the above mentioned problems is found, they will remain purely in the research stage.