Further reading:
Hydrogen Facts All sorts of good things to know about hydrogen.
Fuel Cell Facts  All sorts of good things to know about fuel cells

Hydrogen is the most common and simplest of all the elements.  It has an atomic weight of 1.  However, you wont find hydrogen just laying around, it is almost always bound up with something else.  The most common element on earth it bonds with is oxygen.  This little beastie is Di-hydrogen-monoxide.  It has been known to be fatal if inhaled in quantities as small as a spoon full, can scald in its vapor form, and is the main ingredient in almost all poisons.  You guessed it h20.  Good old water.  However hydrogen is also present in methane (natural gas) and this is where most of today's hydrogen comes from.  Steam reforming of methane produces lots of hydrogen but also lots of co2 a green house gas.  A much better way to produce hydrogen would be to use solar or wind, or in a pinch nuclear (however this comes with its own problems) to electrolyze water.  The equation goes something like this. 

h20 + energy = h2 + o2

So as you can see when you use solar or wind or nuclear to electrolyze "bust up" water you get hydrogen and oxygen.  The oxygen almost always combines with some hydrogen so you also get water vapor.  Lucky for us this process works even better when there is some salt in the water.  If only we could find some place where there is lots and lots of salt water....  

HYDROGEN AS A FUEL

           Because hydrogen is always bound up with something else, it always takes energy to bust it loose.  Because of this hydrogen is not a fuel.  It is a storage medium for energy.  Using solar or wind to bust hydrogen loose from water can be looked at as "storing" the energy from the sun or wind "in" the hydrogen.  Then we can ship the hydrogen around.  Its almost as if the hydrogen is a battery we are using to store up energy to be used later.  But when we are thinking of hydrogen as a "fuel" that is if we are going to use it in a fuel cell or even just burn it, it's great stuff.  When you burn natural gas you get all sorts of harmful bad stuff you would never want to breath in.  And you get a bunch of co2 that causes global warming.  And natural gas is the "cleanest" fossil fuel.  When you burn hydrogen (or use it in a fuel cell) the only thing you get is oxygen and water vapor.  That means if you car ran on hydrogen and you were feeling a little groggy one morning you could take a nice hit off of your tail pipe as a pick me up (I wouldn't recommend doing this with any other kind of fuel)

FUEL CELLS

          So what is a fuel cell?  Well the fancy definition is "an electrochemical device that converts the results of a chemical reaction directly to electricity".  What that really means is it makes electricity without burning something or turning a generator.  This is fun because it means all we have to do is keep pumping in the chemicals it needs to run and we will keep getting energy.  Most fuel cells run on hydrogen (hence why they are mentioned in this section).  Fuel cells like solar cells have a limited amount of power they can put out.  But like solar cells they can be combined together to achieve more power (much like using two "AA" batteries in your walkman instead of one).  This combination is called a stack. 

BENEFITS OF HYDROGEN

          Hydrogen is good because it doesn't produce any harmful byproducts when you use it as a fuel.  It is also the most plentiful element on our planet.  If we use wind or solar (or in a pinch nuclear) to produce hydrogen from sea water, we could easily run just about anything with fuel cells or by directly burning hydrogen.  Many places already have fuel cell busses, and both the UK and California have started to open hydrogen fueling centers.  Soon you could be filling up your car with good old hydrogen and blissfully pumping oxygen and water vapor out of your tailpipe as you went to work every day, instead of the horrible smog that greets most of us now.