1) Its not an energy source (you have to expend energy to get it)
2) Its not very dense
3) Its dangerous.
4) It doesn't matter.
1. Its not an energy source.
Hydrogen doesn't exist around here at ground level by itself. It has to be made. One way to make it is to refine petroleum products, but we're trying to get away from that, so the next best suggestion is electrolyzing water (H2O). Now H2O is the end result after extracting the energy from H2 in a fuel cell or an engine, so really you're just putting the energy in up front so you can get it back later. And that process is never 100% efficient.
Its like Aluminum batteries. Al2O3 exists naturally and the industrial world spends a lot of energy ripping the oxygen off the metal so we can have soda cans and light folding chairs. (As a side note, when people talking about using "spare" capacity from the grid, aluminum refining is actually using most of this extra capacity already.) You can get a lot of energy back out of aluminum by letting it oxidize again in either electric form (batteries), or as heat(think thermite); but you're just cashing out what you put into it before.
There are also some strange nuclear solutions involving thermochemical reactions with water, Iodine and Sulfur; but currently this country seems to be allergic to nuclear power despite some great strides in safety of design and operation (like pebble bed helium reactors).
2. Its not very dense.
All gases have the same number of molecules in a given amount of space. The difference in weights is a matter of how many neutrons and protons a given gas has. H2 is the simplest, and thus lightest gas of all. It also ends up wasting a lot of space for the amount of energy it contains compared to anything else.
In a DOE report, they rated the various fuels in energy density compared with diesel. It went something like this:
Compressed Hydrogen (at 3600 PSI): 6%
NiMH battery: 1.3%
Strangely they didn't list lithium batteries, probably would make compressed hydrogen look even worse.
Basically, their conclusion was that compressed hydrogen would never be practical for cars, and was even a worse idea for things like trucks. (Basically, for a truck, you were replacing an 84 gallon fuel tank, with a giant heavy steel pressure tank four feet in diameter and over twelve feet long. The battery idea wasn't much better: you could get half the needed range with 42,635 pounds of battery, which represented 85% of the weight load of the truck.)
3. Its dangerous.
Dangerous how? The ignition velocity for hydrogen is ten time the velocity for natural gas (and five times that of propane), which means for the same amount of energy, an explosion does ten times the damage.
And because of its density, they're talking about storing it at pressures above 5,000 PSI. A typical welding tank is about a quarter inch thick high strength steel, runs from 1,600-2,400 PSI, and is safety tested for 4,000 PSI; and that amount of pressure is quite dangerous in the event of a rupture. A car with 4 x 5,000 PSI tanks with a rupture would essentially be a car-bomb.
Finally, if burned in an engine, it will actually be a worse contributor towards pollutants such as NOx, because of its high temperature of combustion. Hydrogen burners usually have to use an expensive catalyst in the burner assembly to keep the temperature down. This impacts efficiency as well.
4. It doesn't matter.
The Hydrogen solution is touted for "cars" using a combination of hydrogen fuel, and greater fuel efficiency (since there's not as much power in hydrogen). But lets take a look at the Oil market:
Nasa tried running airplanes on liquid hydrogen, but to make it practical, the equipment size and weight needs to scale down by a factor of over 100. Current research is focused on the factor of five that might make small personal prop planes work (like a Cessna), but even that is facing its own hurdles.
So why tilt at the 5-10% of fuel use going into cars? Its an uphill battle, with no economic advantage. Fuel shortages are coming, and with the corresponding rising prices will come changes in behavior and new solutions.