The energy catalyzer probably does not work. Here is an entry point to some of the criticism: http://tech.groups.yahoo.com/group/H-Ni_Fusion/message/226.
The criticism that nuclear reaction can't take place at low temperature is no good, because Palladium/deuterium does it. Rossi is saying that, like Palladium, Nickel allows for nuclear reactions, except that he has the Nickel/protons fuse together to produce copper instead of the deuterium with deuterium. Fusion of protons with Nickel is an exothermic nuclear reaction (unlike what the previous answers claim), but it is prevented by MeV scale electrostatic barriers, not KeV scale barriers, and is energetically as far from d-d fusion as d-d fusion is from fire.
Rossi's device probably doesn't work, but without a completely sound theory of cold fusion, one cannot be 100% sure. The major problem with the demonstrations that Rossi ran is that the measurements of heat output are done by assuming that all the water that comes into the system is converted to steam, and this is a very unreliable way to measure heat output. You should just use water to measure heat, that's what everyone else does.
Rossi claimed that all the steam coming out of his machine was dry. But dry steam has a huge gas volume, and should rush out in an invisible jet of gas out of his pipe, while his device emitted a "feeble mist" (to quote the linked page). To make mist, all you need to do is to charge water up electrically, so that it breaks into droplets, and that doesn't take any energy at all. The device could be producing no energy beyond the electricity going into it.
Rossi claimed to make copper, and he submitted a sample of Nickel powder with copper and iron inside that he said was the product of his machine. But the copper and iron were analyzed by others and have natural isotope ratios, which is extremely unlikely for the products of a nuclear reaction. The reports of Nickel/Hydrogen cold fusion, unlike Palladium deuterium cold fusion, all come from essentially one place, with no independent reproduction. It is possible that Nickel hydrogen doesn't do anything at all.
But there is no reason to dismiss Rossi a-priori. He claims his device works, and this can be tested by just waiting to see it work.
EDIT: Here is a related answer on the difference between steam and mist； Difference between Steam and Fog / Mist
Here is an update reflecting more recent news: Is the E-cat for real?