Is a "China Syndrome" meltdown possible?
No, any fuel melt situation at Fukushima will be limited, because the fuel is physically incapable of having a runaway fission reaction. This is due to their light water reactor design.
In a light water reactor, water is used as both a coolant for the fuel core and as a "neutron moderator". What a neutron moderator does is very technical (you can watch a lecture which includes this information here), but in short, when the neutron moderator is removed, the fission reaction will stop.
An LWR design limits the damage caused by a meltdown, because if all of the coolant is boiled away, the fission reaction will not keep going, because the coolant is also the moderator. The core will then only generate decay heat, which while dangerous and strong enough to melt the core, is not nearly as dangerous as an active fission reaction.
The containment vessel at Fukushima should be strong enough to resist breaching even during a decay heat meltdown. The amount of energy that could be produced by decay heat is easily calculated, and it is possible to design a container that will resist it. If it is not, and the core melts its way through the bottom of the vessel, it will end up in a large concrete barrier below the reactor. It is nearly impossible that a fuel melt caused by decay heat would penetrate this barrier. A containment vessel failure like this would result in a massive cleanup job but no leakage of nuclear material into the outside environment.
This is all moot, however, as flooding the reactor with sea water will prevent a fuel melt from progressing. TEPCO has already done this to reactor #1, and is in the process of doing it to #3. If any of the other reactors begin misbehaving, the sea water option will be available for those as well.
What was this about an explosion?
One of the byproducts of reactors like the ones at Fukushima is hydrogen. Normally this gas is vented and burned slowly. Due to the nature of the accident, the vented hydrogen gas was not properly burned as it was released. This led to a build up of hydrogen gas inside the reactor #1 building, but outside the containment vessel.
This gas ignited, causing the top of the largely cosmetic external shell to be blown off. This shell was made of sheet metal on a steel frame and did not require a great deal of force to be destroyed. The reactor itself was not damaged in this explosion, and there were only four minor injuries. This was a conventional chemical reaction and not a nuclear explosion.
You see what happened in the photo of the reactor housing. Note that other than losing the sheet metal covering on the top, the reactor building is intact. No containment breach has occurred.
At about 2:30AM GMT on March 14th, a similar explosion occurred at the reactor #3 building. This explosion was not unexpected, as TEPCO had warned that one might occur. The damage is still being assessed but it has been announced that the containment vessel was not breached and that the sea water process is continuing.
Around 7:30AM GMT on March 14th, it was announced that the explosion at reactor #2 has damaged the already limping cooling systems of reactor #2. It may also receive the sea water treatment if they are unable to use a venting procedure to restart the cooling systems.
Is there radiation leakage?
The radiation levels outside the plant are higher than usual due to the release of radioactive steam. These levels will go down and return to their normal levels, as no fuel has escaped containment.
For perspective, note that charts detailing detrimental radiation exposure start at 1 Gy, equivalent to 1 Sv; the radiation outside the problematic Fukushima reactors is being measured in micro-Svs per hour. The highest reported levels outside the Fukushima reactors has been around 1000 to 1500 micro-Svs per hour. This means that one would have to stay in this area for four to six weeks, 24 hours a day, without protection in order to experience the lowest level of radiation poisoning, which while unpleasant is not normally fatal. And this level will not stay where it is.
Also note the chart of normal radiation exposure levels from things like medical x-rays and airline flights.
There have also been very minor releases of radioactive reactor byproducts like iodine and cesium along with the steam. This material is less radioactive than the typical output of coal power plants. It is significant mainly as an indicator of the state of the reactor core.
I read that there's a plume of radioactive material heading across the Pacific.
In its current state, the steam blowing east from Japan across the pacific is less dangerous than living in Denver for a year. If it makes it across the ocean, it will be almost undetectable by the time it arrives, and completely harmless as the dangerous elements in the steam will have decayed by then.
What's this about fuel rods being exposed to the air?
When the coolant levels inside the reactor get low enough, the tops of the fuel rods will be exposed to the air inside the containment vessel. They have not been exposed to the external atmosphere and the containment vessels are all intact.
Can this end up like Chernobyl?
No, it cannot. for several reasons.
Chernobyl used graphite as a neutron moderator and water as a coolant. For complicated reasons, this meant that as the coolant heated up and converted to steam, the fission reaction intensified, converting even more water to steam, leading to a feedback effect. The Fukushima reactors use water as both the coolant and the neutron moderator, which means that as the water heats up and converts to steam, the reaction slows down instead. (The effect of the conversion of water coolant to steam on the performance of a nuclear reactor is known as the "void coefficient", and can be either positive or negative.)
Chernobyl was designed so that as the nuclear fuel heated up, the fission reaction intensified, heating the core even further, causing another feedback effect. In the Fukushima reactors, the fission reaction slows down as the fuel heats up. (The effect of heating of the nuclear fuel on the performance of a nuclear reactor is known as the "temperature coefficient", and can also be positive or negative.)
Chernobyl's graphite moderator was flammable, and when the reactor exploded, the radioactive graphite burned and ended up in the atmosphere. The Fukushima reactors use water as a neutron moderator, which is obviously not flammable.
Note that while Chernobyl used light water as a coolant (as distinct from heavy water), it was not a "light water reactor". The term LWR refers strictly to reactors that use light water for both cooling and neutron moderation.
The news said this was the worst nuclear power accident since Chernobyl, though.It's the only nuclear power plant accident of its type since Chernobyl. It's easy to be the worst in a sample size of one.
Is this like Three Mile Island?
There are similarities. The final effect on the world is likely to be similar: no deaths, minimal external contamination, and a tremendous PR disaster for the nuclear industry due to bad reporting by the media.