No, no Chernobyl yet. What's missing from this to make it something like that is an explosive release of the core materials. Chernobyl didn't even melt down -- they used a reactor that used graphite rods instead of water to cool the system. Graphite burns at a certain temp, so you can't ever let that kind of reactor (no longer used, for obvious reasons) get hotter than that or it's game over. The Chernobyl scientists were running an experiment on what would happen if they did this or that and in the process got the graphite hotter than it's burn temp, causing the plant to blow up. So you had raw nuclear fuel (that lethally doses you with radiation within seconds if you were standing next to it) laying here and there thousands of meters from the plant.
Right now, with the exception of the spent fuel pool, all the rods are contained inside vessels. Some of those vessels are apparently compromised, but none of them are at risk of asploding. They have all partially melted down more or less and will probably fully melt down before it's all over, but even then it should be a very localized problem.
Now the spent fuel pools -- those seem like some of the dumbest engineering you could imagine. They sit inside the reactor at the TOP of building. They contain lots of spent fuel rods, all of which are highly radioactive -- same kind of deal, you stand near it for a few seconds when the pool is empty, it's time to sign your will. The buildings that housed these pools EXPLODED. So now all that stands between the fuel rods and the light of the moon is a pool of water.
Reactor #4, so it seems, was down for maintenance, so they put all their live fuel into the #4 spent fuel pool. So in addition to old spent fuel, you have young, hot, completely fissionable fuel sitting in there. According to the U.S. Nuclear Regulatory Committee chairman, all that water has now boiled away. Japan denies this, but really, who are you going to believe at this point?
The upshot to this is that now all that fuel is slowly melting down with NO containment. Any byproducts of this go right up into the air. Workers can't approach it because of the radiation. They can't even fly a helicopter over it to dump water on it because of the radiation.
Worst case scenario at this point, which I've read is unlikely (like almost all the other things that have happened thus far) is that the spent fuel rods go re-critical, i.e., start fissioning again. That would be worse than Chernobyl by a large factor, as this fissioning would probably produce a small explosion (not like a nuclear bomb, more like a conventional bomb) that would propel a crapload of nuclear fuel thousands of meters from the building. That fuel could only be cleaned up by robots or people who are willing to sacrifice their life, a 'la Chernobyl. It would also render the area around the plant uninhabitable for many generations.
They have countermeasures in place that are supposed to prevent re-criticality, such as the geometry of the spent fuel pool itself and the racks that hold the rods, which are heavily laced with boron (which inhibits fissioning).