Why is there a scarcity of lithium? One of the major impediments to the widespread adoption of electric cars is a shortage of lithium for the batteries.  I read an article a while back that says that there is simply not enough lithium available on the entire planet to make enough batteries to replace every gasoline-powered car with one electric car.  And that confuses the heck out of me.
The Big Bang theory says that in the beginning, there was a whole bunch of hydrogen, and then lots of hydrogen started to clump together and form stars, and those stars produced lots of helium through fusion, and then after helium, all the rest of the elements.  That's why hydrogen is the most common element in the universe by far, and helium is the second most common.
Well, lithium is #3 on the periodic table.  By extrapolation, there ought to be several times more lithium around than, say, iron or aluminum, which there is definitely enough of for us to build plenty of cars with.  So why do we have a scarcity of lithium?
 A: Actually, what you've read about the production of nuclei is not quite correct. There are several different processes by which atomic nuclei are produced: 


*

*Big Bang nucleosynthesis is the fusion of hydrogen nuclei to form heavier elements in the early stages of the universe, as it cooled from the big bang. There are rather specific thermal requirements for this process to occur, so there was only a short time window in which heavier elements could form, meaning that the only fusion to actually happen in significant amounts was the conversion of hydrogen (and deuterium) to helium, and an extremely tiny amount of lithium.

*Stellar nucleosynthesis is the fusion of hydrogen and other nuclei in the cores of stars. This is something separate from big bang cosmology, since stars didn't form until millions of years into the universe's lifetime.
Now, contrary to what you might have read, not all elements are formed in stellar nucleosynthesis. There are specific "chains" of nuclear reactions that occur, and only the elements that are produced by those reactions will exist in a star in appreciable quantities. Most stars produce their energy using either the proton-proton chain (in lighter stars) or the CNO cycle (in heavier stars), both of which consume hydrogen and form helium. Once most of the hydrogen has been consumed, the star's temperature will increase and it will start to fuse helium into carbon. When the helium runs out, it will fuse carbon into oxygen, then oxygen into silicon, then silicon into iron. (Of course the actual process is more complicated - see the Wikipedia articles for details.) Several other elements are produced or involved along the way, including neon, magnesium, phosphorous, and others, but lithium is not among them. In fact, stars have a tendency to consume lithium, rather than producing it, so stars actually tend to have only small amounts of lithium.

*Supernova nucleosynthesis is the fusion of atomic nuclei due to the high-pressure, high-energy conditions that arise when a large star explodes in a type II supernova. There are certain similarities between this and big bang nucleosynthesis, namely the high temperatures and pressures, but the main difference is that an exploding star will have "reserves" of heavy elements built up from a lifetime of nuclear fusion. So instead of just forming a lot of helium as occurred just after the big bang, a supernova will form a whole spectrum of heavy elements. In fact supernovae are the only natural source of elements heavier than iron, since it actually requires an input of energy to produce those elements as fusion products. I believe some amount of lithium would be formed in a supernova along with all the other elements, but since a large star would have used up its hydrogen and helium in the central region where most of the action takes place, lithium is probably not a particularly common reaction product.
A: The answer is that nucleosynthesis routes to produce lithium in stars require temperatures that are far higher than the fusion reaction that readily destroys lithium inside stars.
Lithium is a scarce element in the universe and the abundance of Li in the Solar System and in the Earth's crust is low compared with elements like carbon, oxygen, silicon and iron.
The Solar System lithium is created partly (only 10%) by primordial nucleosynthesis, a bit by spallation reactions of cosmic rays on nuclei in the interstellar medium, but mainly in the interior of relatively low-mass asymptotic giant branch (AGB) stars and in nova outbursts (e.g. Prantzos 2012). The main reaction mechanism is the fusion of helium-4 and helium-3 to produce beryllium-7. This then undergoes electron capture to lithium-7.
Whilst there is plenty of helium-4 inside stars there really isn't much helium-3, except where it is produced in hydrogen-burning cores/shells, but these regions are also hot enough to quickly destroy lithium-7 through proton capture back to helium-4 nuclei. Thus one needs special conditions where Be-rich material from the core/shell is mixed upwards and undergoes electron capture in regions cool enough for the Li to survive (Cameron & Fowler 1971).  This can happen in "hot bottom burning" AGB stars with masses of about $4<M/M_{\odot}<8$, which are undergoing shell H- and He-burning for some of the time (e.g. Garcia-Hernandez et al. 2013). The convective envelope reaches down to the H-burning shell, dredges up Be-rich material, which then becomes Li-7. The process is of limited efficiency, since the same convection takes a lot of the Li-7 back down again to be burned. So, although AGB stars can efficiently blow enriched material into space through their massive winds, the material isn't that enriched with Li.
The Cameron & Fowler mechanism can also take place in novae explosions occur when matter is transferred from a companion onto the surface of a white dwarf and detonates. The accreted material needs to have helium-3 in it, so must also have come from regions where there has been incomplete hydrogen burning. Fast, explosive ejection of a Be-rich shell then results in enrichment of the ISM with Li-7. It turns out that the special conditions required to accrete material with lots of He-3 do not result in enough Li production to boost the interstellar medium Li abundances beyond what we see.
But I think the main thrust of the question is why isn't Li just produced from some sort of fusion reaction, like helium or carbon?
The answer is that it is! For instance Li-7 is produced as part of the PPII branch of the pp chain, at temperatures between $1.4\times10^7$ K and $2.3\times 10^{7}$ K. But at these temperatures the Li-7 is rapidly fused with a proton to form two He-4 nuclei.
So the basic problem is that in stellar interiors, Li-7 is readily burned at temperatures above $3\times 10^{6}$ K, but any fusion reactions that produce Li (or elements heavier than Li) require much higher temperatures than this.
A: The common mistake behind this statement is that lithium is seen as a fuel that's consumed and discarded. After all, that's how oil works. There's not enough cheap lithium for that. But like steel, lithium will be recycled.. 
A: The key word in what you've heard is "available" because there is quite a lot of lithium in the earth that is not so easy to obtain.  The notion of "available Lithium" probably means known land reserves, which according to this page amount to 14 million tons.
The amount dissolved in seawater is estimated at 230 billion tons (which is enough for lots of batteries).  Seawater extraction does not seem to be economically viable yet, but people are studying it.
The estimated concentration of lithium in the Earth's crust ranges from 1 to 31 ppm, so if we excavate the whole crust, we'll get between 20 and 600 trillion tons.  In other words, if our civilization ever came to a point where we really needed lots of lithium, we wouldn't have to go too far to find it.
A: Lithium is more abundant in the Earth's crust than lead. However, it is more reactive than such metals and less abundant than other reactive metals such as sodium. Because of this it does not tend to accumulate in rich geological deposits in a form that makes it easy to extract. Its lightness may be another factor.
Reactive metals such as lithium can form salts which dissolve in water. These are then left in deposits when enclosed areas of water dry up. Lithium is 1000 times less abundant in the Earth's crust than other reactive metals such as Sodium, Calcium and Potassium so it is still only found in relatively small quantities in such deposits.
However, some compounds of lithium are sufficiently soluble that it is present in some dried up sea deposits. About half the accessible Lithium on Earth is said to be beneath the Bolivian dessert and if extracting it in the future becomes as important as extracting oil is now, then there is not likely to be such a big shortage. 
A: According to this NPR story, there is no shortage of lithium for batteries:

"I don't know of any serious person in
  the automotive industry or in the
  lithium industry who believed that
  there is a serious, long-term supply
  problem," he says. "In fact, for the
  next 10 years there will probably be
  an oversupply of lithium because so
  many companies have now moved into the
  market."
And unlike the impact of mining other
  natural resources, concentrating
  lithium is an "environmentally benign"
  process, Fletcher says. "It's about as
  low-impact as mining can get. They're
  really just pumping water up ... and
  there are really no toxic chemicals in
  a lithium-ion battery."

A: This is a small complement to David's and Scott's answers
As usual Wikipedia's page on Lithium contains useful information :

Both natural isotopes have anomalously low nuclear binding energy per nucleon compared to the next lighter and heavier elements, helium and beryllium, which means that alone among stable light elements, lithium can produce net energy through nuclear fission. The two lithium nuclei have lower binding energies per nucleon than any other stable compound nuclides other than deuterium, and helium-3. As a result of this, though very light in atomic weight, lithium is less common in the solar system than 25 of the first 32 chemical elements.
[...]
⁷Li is one of the primordial elements (or, more properly, primordial nuclides) produced in Big Bang nucleosynthesis. A small amount of both ⁶Li and ⁷Li are produced in stars, but are thought to be burned as fast as produced. Additional small amounts of lithium of both ⁶Li and ⁷Li may be generated from solar wind, cosmic rays hitting heavier atoms, and from early solar system ⁷Be and ¹⁰Be radioactive decay.

So, basically, Lithium is (barely) produced as David Zaslavsky told you in his answer, and the reason the production is low because Lithium is barely stable.
But as @Scott Carnahan tells in his answer, the notion of lithium scarcity is linked with its repartition on earth. And the reason it is difficult to obtain is ultimately its  high chemical reactivity, which means that it is basically diluted everywhere, and is rarely concentrated in easy to mine deposits.  On the same wikipedia page as above, they say :

Although lithium is widely distributed on Earth, it does not naturally occur in elemental form due to its high reactivity.
[...]
According to the Handbook of Lithium and Natural Calcium, "Lithium is a comparatively rare element, although it is found in many rocks and some brines, but always in very low concentrations. There are a fairly large number of both lithium mineral and brine deposits but only comparatively a few of them are of actual or potential commercial value. Many are very small, others are too low in grade."

