Cecil Adams' answer isn't bad, but he does overlook something very important. He writes:
But Cecil, you object, how is this thought supposed to be comforting? Today we don't have any comparable alternative fuel waiting in the wings. Sure we do. What's more, it was waiting in Hubbert's day. The title of his 1956 paper was "Nuclear Energy and the Fossil Fuels." His purpose in writing had been to point out that, in contrast to oil, the U.S. had sufficient reserves of fissionable fuels, chiefly uranium, to last hundreds and likely thousands of years.

He neglects to mention that nuclear energy isn't going to affect the transportation issue, which is arguably where the most important breakdowns will occur. But maybe Adams was too reluctant to claim that hydrogen or electric cars are going to save us.
That assessment of "hundreds to thousands" of years of course takes inventing breeder nukes. Since the natural fissionable uranium is 235 at .7 of a percent, we need to efficiently make the U-238 into Pu-239 to use. Also, with breeders, we can use thorium by making it into U-233, an artificial fissionable. You need to isolate U-235 (already done) to get the ball rolling once you invent a breeder.

Of course, you don't want idiots to get any of the fissionables, as they can get a bang out of them. This is the biggest problem of nukes in general. Breeders mean that you can recycle waste most-way. Spent fuel is mostly U-238 with some Pu-239 added for flavour from normal reactors. The Pu-239 comes from neutron bombardment of U-238 during use. A "perfect" breeder would end up making waste made of fission byproduct elements about half the atomic weight of the fissionable.

As above, fission has its problems, but nothing is problem-free. I'd rather risk an occasional Chernobyl vs. the certainty of global warming with using up the coal. With fusion, all bets are off. It could take centuries to figure it out - assuming we keep civilisation up and running! (and that's a dangerous assumption!)

Of course, you don't want idiots to get any of the fissionables, as they can get a bang out of them

Of course, many would argue that many of the world's leading idiots already have fissionables.

Unfortunately, ONE idiot does have fissionables, in the form of the remote to use the fissionables. That is guarenteed, until 1/20/2009. (at 11:59:59AM DC time) Barring the possibility of this idiot seizing power in a coup-like action.
One alternative is a slightly improved CANDU reactor (using heavy water) with a lot of thorium mixed in between the convential fuel.  1:1 breeding (no extra fuel for other reactors like French Phoenix, etc.) but no real depletion either.

From my Physics background (decades ago), U-233 is not an ideal bomb ingredient but can be made to work with an effort.

Bush has decided to push MOX recycling (do not seperate all of the relatively short lived and intensely radioactive elements above Pu).  These elements have some fuel potential as well.  The heat and radiation from these make fabrication from stolen fuel "problematic".

Estimates of fuel reserves are with current technology & prices.  Uranium has been prospected for and mined for only a few decades; much less than most other minerals.  No interest in new sources for two decades or so.

Fission reactors have considerable prospects for that "New Technology Silver Bullet", unlike oil.

BTW: Used fuel may become a good source of platinum group elements (when U atoms split, they do so in a variety of ways).

He neglects to mention that nuclear energy isn't going to affect the transportation issue...
Not by itself, no.  But there are so many Li-ion battery technologies either already in production or just about to hit, plus supercapacitors, plus the Firefly revision of the venerable Planté cell, that this problem should not be regarded as a roadblock.  Sure, any one of these technologies could have something which prevents it from becoming cheap enough... but all of them?
At least Li is a fairly common element. What would be good as far as common-elements concerns, would be a "Sodium-ion" battery. Might be heavier, but may pack a decent punch like the Li-ion cousin. But that may be a wish, as Li is liable to get scarce or expensive, while Na is "dirt cheap".

Lithium is fairly expensive. A lot of the cost is processing raw material to get it. Making sodium and aluminium has the same problem. Electrolisis is a major cost.

How nukes can serve transportation is to have electrified mass transit. Buses and trains, both passenger and freight. No fun, but a commute is possible. Battery cars (any battery) may be rich peoples' toys in the long run. One good thing about extensive mass transit is that drunk driving will no longer exist.

One good thing about extensive mass transit is that drunk driving will no longer exist.
Don't be so sure; running buses and trains is a very boring job, and the personnel have been known to use substances to make their time more bearable.
OK, you got me. :) What I meant, of course, was that it would cease to be a major problem becuse commoners wouldn't be driving. With a vastly smaller pool of drivers, it would almost stop being a problem. In a virtually car-free future, drunk driving will be as rare as that other type of drunk bus driver, the drunk airline pilot. Laws could be zero tolerance. A bus, train, or aircraft operator gets caught, and they lose all vehicle operator priviledges forever. Attrition will reduce it nicely. Want to drink? Don't drive!