Here's the main problem evolutionists encounter when dealing with this question: whether or not creationism/ID can be falsified depends on how specifically they define their god or "intelligent agent."
Let's take the following issue, for instance: If ID is unfalsifiable, how can scientists claim to have falsified proposed examples of irreducible complexity (IC)? To see why scientists are in fact perfectly justified in doing so, let's look at the claims of ID and IC more closely. ID states roughly, "Life was created by an intelligent designer." IC states roughly, "Biological systems exist that could not be created naturally through the iterative addition of parts."
The first thing to note is that IC isn't so much an attempt to prove ID as it is an attempt to disprove naturalistic evolution. But more importantly, ID does not by any means require IC. If the concept became so bankrupt that even IDists had to abandon it, they would just claim that a designer (for some reason) created only life that could also have been created via step-by-step addition. Thus if IC is falsified, the larger thesis of ID would be a bit weaker but still quite intact.
IC (or at least alleged examples of it) can be falsified; ID as commonly argued cannot. There's no contradiction here: it's simply the case that an unfalsifiable argument contains a falsifiable (and in this case only somewhat related) sub-argument.
Let's use the argument from poor design as another example. Many critics reasonably assume that an all-powerful, all-knowing, all-good creator would design his creation as skillfully as possible. Well, we know of many instances of suboptimal design in nature—the eye and the vermiform appendix are two examples that can be found in humans. So the God hypothesis has been falsified, right?
Not if the creationists have anything to say about it. Those attempting to go the secular ID route will simply claim that (for some reason) the designer didn't make creatures as flawless as he could have. Those of the more fundamentalist bent will often claim that suboptimal design is the result of sin "entering the world" as a result Adam and Eve's disobedience to God. Either way, an entire class of counterexamples has been conveniently explained away.
The Miracle Retreat
Young-earth creationism is a treasure trove of falsified claims. Biology, geology, cosmology and many other fields of science have shown that the earth and universe are many thousands of times older than YECs require. But at any point, all they have to do is resort to supernatural intervention as an explanation, and their worldview becomes instantly untouchable. Fossil record getting you down? Just say the devil planted the bones there to fool you, or that God put them there to test your faith!
The Omphalos hypothesis takes this to an extreme: maybe God created the universe with the appearance of age in the most intricate detail. From geological formations to starlight to the ancient junkyard of genes in each of our cells, God could have set everything up so that the universe appears to be 14 billion years old even if it's only a few thousand. If a YEC accepts this possibility, no mountain of empirical evidence could budge them from their position.
So, is creationism unfalsifiable? It depends. In some cases we can falsify components without affecting the falsifiability of the whole. And we can attempt to falsify the rest. However, creationists can respond by either defining the creator as vaguely as possible or claiming that he used miracles to simulate the evidence. Their ability to move the goalposts at will demonstrates that their position is unfalsifiable in practice.