First, I need to point out that the news about the "10 million times higher radiation" that spread across the world media today were just an error. TEPCO revealed that the error came from a misinterpretation of the concentration of cobalt-56 as iodine-134. Because of this fixed mistake, it's completely plausible that iodine-134 was never detected over there, and there was just cobalt-56. However, let me continue with the bulk of the answer that was written before the mistakes in the reporting began to be appreciated.
Chernobyl and similar accidents have been usually associated with iodine-131 (half-life of 8 days) as the primary source of thyroid cancer. However, iodine-134 (and other isotopes) is usually produced in greater quantities. Its immensely short lifetime makes it quickly irrelevant, however.
On the other hand, when one studies "acute" (and therefore also short-lived) problems with high radiation, such as the "10 million times increased radiation in the water" today, the quickly decaying isotopes such as iodine-134 are just dominant.
Where do nuclei such as iodine-134 come from? Well, there is fission going on in the reactor, so fissiles such as uranium-235 are broken into pretty much arbitrarily smaller pieces and iodine-134 is often among them. See
for the typical products of fission - the mass is often divided in the 3:2 ratio etc. so isotopes such as iodine-134 are common. Yes, iodine-134 is a direct product of fission but most likely not ordinary neutron-driven fission but probably only photofission (fission initiated by gamma rays hitting the large nucleus), see these papers for details:
If the uranium-235 splits into a $Z=53$ iodine isotope and one more, this "one more" has to be yttrium with $Z=39$. The half-life of yttrium-99 and nearby isotopes you may get (after emitting a few neutrons) is comparable to a second.
Why is exactly iodine-134 so much more represented among the fission products than other iodine isotopes? Well, because it has the rigth proton-neutron ratio. The fissile, uranium-235, has $Z/A$ equal to $92/235$. And because iodine's $Z=53$, the same ratio of protons and neutrons - a democratic fission - is obtained for the total nuclear mass
$$ 235 / 92 \times 53 = 135.4.$$
So it's most likely to produce iodine isotopes whose $A$ is close to 135. Iodine-135 has 6.6 hours of half-life, so it's not that important "acutely", while iodine-136 has 83 seconds and disappears too quickly. It just happens that the contamination of water, as was measured, is dominated by half-lives close to 1 hour, and iodine-134 is the key representative in this realm.
Other elements, different from iodine, have typically much longer lifetimes for the same $Z/A$ ratio. Still, it's plausible that much of iodine occurs from decay of other fission products, e.g. from beta-decay of tellurium-134 (see the other answer): fission directly prefers to produce even $Z$ elements while iodine has $Z=53$, odd. But this even-$Z$ rule is not "strict".
Otherwise, fission is a messy process and it can produce "almost anything" in the list of isotopes. Again, just to be sure, fission is not about getting incremental alpha and beta decays only; it's the process of splitting the large nucleus into two comparable pieces.