Either nothing at all or something terrible. It all depends on one thing: Are the containment vessels still sealed?
Before we go on, I am not a nuclear engineer, nor am I going to declare myself an expert on nuclear design. Take this with a grain of salt and do your own research if you doubt me.
Every modern western-designed (read: Non-Soviet) reactor has three main components: the core, the reactor vessel or pressure vessel surrounding the core and the containment vessel.
These plants are designed according to a defense in depth philosophy. The idea is that you have a way to keep things relatively benign up until everything has gone wrong at a certain stage, then you have a chance to keep them relatively benign at another stage, even though it's pretty bad for the reactor's owners to have to move to the next "ring" of defense. The rings are cooling, containment in the reactor vessel (and probably more cooling) and containment within the containment vessel.
If cooling fails for a short time, you may have some melting of the rods and damage to the core equipment. No danger to the public, but costly for the folks that own the reactor.
If there's a long-term cooling failure, you may get much or all of the core turning to superheated slag, but it stays in the reactor vessel. What happened at Three Mile Island was in this stage, with half the fuel melted by four hours after the first alarms went off. Here's a graphic of what was inside the pressure vessel:
However, the vessel contained the core.
If everything goes completely wrong you can have a total meltdown. All the fuel is reacting and the core is a glop of superheated molten uranium with some melted metals from the core's structure in it. This will melt through the bottom of the pressure vessel in short order.
This is where the containment vessel comes in. It's designed to contain a total meltdown. The glop settles to the bottom of the vessel, spreads out and cools by simple convection. It will be years before the power company can even get inside to clean it up, but there is no China Syndrome (at Chernobyl the molten core didn't even melt a steampipe it poured through on its way to the basement), and all the radiation is kept away from the public and the environment. In a partial or complete meltdown there will be some releases of radiation (sometimes you need to release pressure or get rid of hydrogen and venting it is the only way) but the real problem is contained.
So, here's where we come to the answer to your question: If the reactor vessels at Fukushima are intact, the worst case is that these reactors will melt to slag and sit in a pool at the bottom of the containment vessel for about ten years or more. If they aren't intact, there will be environmental contamination. Lots of it. Chernobyl? Unlikely, but it would be bad. How bad depends on how compromised the vessels are and where. And the problem is, the earthquake that occurred was about 16 times worse than the worst case the plant was designed to withstand. So we may have a cracked containment vessel or two.
One of the problems is that we've never been here before. Chernobyl was so much worse, and Three Mile Island is overblown, with people in the area getting less radiation than a chest x-ray after the crew screwed up in almost every way possible due to poor training and bad control systems design.
