Some of those sympathetic to intelligent design (ID) argue that science as it’s currently taught assumes naturalism, and further that science tries to rule out ID as unscientific on the grounds that ID invokes the supernatural.  But science makes no claims about naturalism. Scientists simply propose explanations which are accepted or rejected on the basis of their scientific merit.
Intelligent design fails as science not because science a priori rules out the supernatural (methodologically it doesn’t need to do this, and in fact wastes no time on the matter), but because the intelligent design hypothesis has no merit as a scientific explanation.
Because science doesn’t presume naturalism, there’s no basis for supposing it violates any U.S. constitutional prohibition on states favoring or establishing a particular religious or philosophical view. So ID need not be imported into the science curriculum to provide "balance" or give non-naturalistic views "equal time." Because ID conclusively fails as good science, it should not be presented or taught as a viable scientific alternative to Darwinian accounts of evolution. But ID could usefully be discussed as good example of a failed scientific hypothesis, helping to clarify what science actually is, and does.
Below, I’ve set out what I take to be some fairly uncontroversial, central characteristics of legitimate scientific explanation, and then list reasons why ID doesn’t embody or exemplify these characteristics. I don’t pretend that these are exhaustive, that they aren’t redundant to some extent, or couldn’t be improved upon in many respects, so I invite interested parties to improve upon them (e.g., see here for Mike Beyer's nice synthesis of the 10 characteristics listed below). But it’s crucial to note that in characterizing science, none of the points below invoke the natural/supernatural distinction. By virtue of its aims and methods, science ends up producing a unified view of the world, what we call nature, but it doesn’t start out with ontological assumptions that make it partisan to naturalism.
A first cut at some basic characteristics of scientific explanation
Other things being equal, science seeks the simplest and most parsimonious peer-reviewed explanations, based on empirical, intersubjective evidence.
Science tries to minimize the number of unverifiable or ad-hoc assumptions in constructing explanations.
Science is conservative in hypothesizing new explanatory factors: to the extent possible, explanations will be sought among phenomena already known to exist before positing other phenomena as explanatory factors. Science is not unnecessarily inflationary in its ontology.
Science seeks testable, verifiable, and transparently mechanistic or specifiable explanations for phenomena - no mysterious or unspecifiable processes play a more than a passing role in scientific accounts.
Entities accepted by science are either directly observed or indirectly inferred via experiment or theory, where such inference predicts specific characteristics of the entity that can be tested for in later experiments or that bear on other predictions.
Science seeks explanations which connect phenomena with one another, which unify different levels and domains of phenomena, and which generate testable predictions. Good scientific explanations are in these senses productive.
In science, an explanation can’t simply be posited to match the target phenomenon in order to fill an explanatory gap - there has to be independent evidence of the features of the explanation, including any hypothesized cause or causal agent.
Before positing explanatory factors that have no other empirical support besides their function of filling an explanatory gap, science will declare the target phenomena to be as yet not fully explained.
Science will put stock in a provisional, as yet incomplete explanation involving known processes and entities rather than in an explanation which claims completeness at the cost of invoking ad-hoc, disconnected, and mysterious entities and processes (see 2, 3, 4 above).
Science seeks explanations for all phenomena in its purview; it always asks what determines the characteristics of any phenomenon that figures in its explanations, including hypothesized causes or causal agents: how did that originate, what explains that?
Note: see Mike Beyer's synthesis of these 10 points into 4 essentials of scientific explanation: coherence, verifiability, transparency, and simplicity.
Why intelligent design (ID) isn’t good science
(The corresponding points above are in parentheses):
ID leaves the designing intelligence unexplained in the same way as ID claims that "irreducible complexity" is left unexplained by Darwinian selective processes, but worse, since it offers no specific hypotheses or mechanisms. ID hasn’t produced an explanation, it simply pushes the demand for explanation back a step and so is otiose. Thus:
ID posits an extra entity unneeded for explanation, so violates parsimony and simplicity (1).
ID seeks explanations outside of well-substantiated, empirically-supported phenomena without fully investigating the adequacy of explanations which restrict themselves to such phenomena. ID is thus not conservative in its explanations, but is instead inflationary  (3, 8, 9).
ID doesn’t specify how design is carried out: no mechanism or process is proposed, and further, no means of discovering this mechanism is proposed. The mechanism remains unacceptably mysterious with no hope of being clarified (4).
ID supplies no observational or inferential evidence for a designer that specifies or predicts its specific characteristics. (5).
Since no mechanism or process is shown by which intelligent design works, the designer posited by ID is left unconnected to other phenomena (6).
ID lacks any explanatory or predictive power; it is unproductive  (6):
- ID doesn’t predict biological features that arise as change occurs in organisms.
- ID doesn’t explain the particular biological mechanisms that are found in organisms.
- ID can’t explain patchwork, jury-rigged, or sub-optimal organic "designs." 
- ID doesn’t suggest any experiments to prove the design hypothesis.
- The designer assumption does no real explanatory work; it simply pushes the question further back (1, 3).
ID provides no independent evidence for the designer beyond its purported explanatory function (i.e., to fill the explanatory gap), so the designer is just an ad-hoc explanatory posit, like elan vital, phlogiston, etc. (7).
In leaving the designer unexplained and its characteristics unspecified, ID fails to treat the designing intelligence as a possible object of scientific explanation (10).
On proving a negative: In general, ID is a negative thesis - that standard evolutionary explanations cannot, however well elaborated, account for some particular phenomena, e.g., "irreducible complexity." The plausibility of the design hypothesis is thus only a function of the purported failure of selectionist explanations. But there is no argument to support the idea that selectionist explanations will not or cannot be completed, especially as biological mechanisms become better understood, and indeed many selectionist explanations are complete to the satisfaction of many scientists. This means, if selectionist explanations are completed and filled out to a reasonable degree (what’s reasonable is of course a bone of contention), then the intelligent design hypothesis loses this sort of support. The same goes for the origins of life: once a plausible mechanism is established, then ID becomes otiose.
On falsifiability: It is often supposed, although not universally agreed, that scientific hypotheses and conjectures are at least in principle falsifiable, if not directly testable. In contrast, ID is unfalsifiable: no experiment could prove or disprove it. ID simply says that what selectionism or other science can’t explain is explicable by appeal to design, so ID can always fill the gaps left by science: thus there’s no way to prove it wrong. (This point is taken from Larry Arnhart’s piece" Evolution and the New Creationism: A Proposal for Compromise," Skeptic V8#4, 2001, p. 48.)
On low probability events: Science accepts the possibility that certain events and conditions may have been extremely low probability occurrences, but doesn’t draw any ontologically inflationary conclusions from this. In contrast, ID draws the inference that since (let us concede for the sake of argument) it’s highly improbable that the universe has constants which are favorable to life, or that life arose at all, there must have been an intelligent agent that chose the constants and/or created life. But this inference simply begs the question of the prior probability of the existence of the designer.
2. "Enthusiasts for ID ignore the growing laboratory evidence for the selection of biological function from random collections of proteins and nucleic acids. Molecular biologists and biotechnologists have shown that selection acting on randomly generated libraries of billions or trillions of biological polymers, such as peptides or RNA molecules, can produce molecules with useful biological functions, such as specificities for small ligands or catalytic activities. Computer scientists, complexity theorists, and even physical chemists have also documented striking examples of order that develops spontaneously. It is simply no longer tenable to equate order, complex structure, or sophisticated function uniquely with conscious design." From Greenspan, N. S., "Not-So-Intelligent Design," The Scientist 16 :12, March 4, 2002.
3. "A truly fundamental problem with the notion of ID, as a scientific idea, is that, ultimately, it has effectively no explanatory or predictive power. Suggesting that an unknown Intelligent Designer of unspecified attributes designed the eye, the clotting cascade, or the immune system offers no scientific insights into these biologic marvels and suggests no incisive experiments." Ibid.
4. In response to this objection, Michael Behe has posited an aesthetic motive which prompts the designer to put "flaws" in his creations, but this assumes just those characteristics of a designer needed to explain design, so is ad-hoc (2). This point is taken from Larry Arnhart’s piece "Evolution and the New Creationism: A Proposal for Compromise," Skeptic V8#4, 2001, p. 49.
TWC, March 2002, revised July 2009