I'm not especially comfortable with such categories. Taking the categories of faulty science first, a little thought suggests that there are a number of ways that some scientific idea or hypotheses can be wrong. A hypothesis can simply be mistaken, though plausible given available knowledge at some point in time. Even the very best scientists can make such mistakes, especially regarding phenomena that have not been amenable to proper research at the time. The concept of a "luminiferous aether", prior to the Michelson-Morley experiment, is a suitable example. Even Einstein made this kind of mistake, for instance in believing that the universe was static rather than expanding, before Edwin Hubble demonstrated otherwise.
But "bad science" is something worse than mistaken. It is an idea or hypothesis that is based on errors in methodology or reasoning or understanding that a competent scientist simply should not make, given available knowledge at the time. "Intelligent design" may be the canonical example of this sort of thing, but there is no lack of other examples throughout the history of science.
"Not even wrong science" is even worse. It's usually the product of an earnest, well-meaning individual who has an enthusiasm for some branch of science, but hardly any actual training or understanding of the subject. Examples of this sort of thing include cosmological theories involving "dynamic energy vortices", "proofs" that the theory of special relativity is obviously wrong, etc. Alternatively, some would place in this category any purportedly scientific theory that has no testable predictions -- superstring theory being a favorite (alleged) example. I won't get into that debate right now.
But then where do we put other kinds of "bad science"? For instance, plausible results which are nevertheless fraudulent because the experimental data has been fudged or simply fabricated. Some, but not all, of Korean stem cell scientist Hwang Woo-suk's work is the currently best-known example. Or how about the "results" of scientists employed by tobacco companties, which failed to find a link between smoking and lung cancer?
Many people use the term "junk science". Where does that fit in? Unfortunately, it's used rather loosely, sometimes in good faith and sometimes not, by anyone who wants to disparage unwelcome scientific claims. Both believers and skeptics of human-caused climate change use the term to describe the claims of their adversaries.
But enough about "bad science". You can find many lists of alleged examples, for instance at the site appropriately called Not Even Wrong. (That's the work of Will Kinney, rather than the perhaps better-known blog dedicated to arguments against superstring theory.) See also the newwpaper column called Bad Science, by Ben Goldacre.
But I've gone on much longer than I intended to regarding bad science. What about "good science"? Can we consider it to be any science that is fairly generally accepted as being correct? I'm not comfortable with that either. The problem is that there's no good set of operational criteria for certifying some scientific theory to be "generally accepted as correct". Indeed, for any given scientific theory or claim, there's a whole spectrum of confidence about whether the results can be considered as "proven".
Of course, there are certain necessary conditions a theory must meet in order to be considered "good science". It needs to be internally consistent and consistent with other "facts" that are also considered to be "known". (That can be a can of worms.) It needs to be falsifiable (i. e. there has to be some conceivable experiment that could rule out the theory). There ought to be at least some evidence that actually supports the theory. And so forth.
Finding sufficient conditions, however, for a theory to be considered "good science" is a lot harder. I'll present a list, in a moment, that offers several examples. The overall point is that for any given theory, it is often reasonable to regard both the theory and its negation as plausibly correct to some extent. Which means that both the supporters and opponents of a theory can be reasonably regarded as advocating "good science", even though at least one side is actually wrong... if and when we could determine the "real" truth.
And so, I tend to regard as "good science" any reasonable, plausible hypotheses that meet the necessary conditions and have "some" evidence in their favor, even if they haven't yet been fully "proven". Do we need to have a name for this category, such as "good but not fully proven science"? I don't know, because in fact most hypotheses which are still being researched naturally reside in this category -- even if they are pretty generally accepted as correct.
Herewith, some examples (I won't clutter this up with links to Wikipedia, but you may consult it, or the reference of your choice, for names and terms you're not clear about):
1. Black holes. At first almost everyone, even Einstein, thought this was a crazy idea. Eddington nearly destroyed Chandrasekhar's career over this issue, though the evidence for black holes, lately, has been pretty darn good. But there are still doubters, and very recently a proposal has been made that could give an alternative account of black holes, and the controversial theories of dark matter and dark energy as well. See here.
2. Dark energy/cosmological constant. Although a small cosmological constant used in the Friedmann equation gives a very good fit with universe expansion data from supernovae, other (still quite controversial) observations of very distant gamma-ray bursts do not fit. And there are alternative accounts -- see above, and for a different one see here.
Further, there is no decent theoretical explanation of a small cosmological constant.
3. Dark matter. The evidence for this is very good, and of many kinds. Yet many people keep trying to come up with alternatives. Again see above. A very reputable physicist, Jacob Beckenstein, has recently claimed to have reconciled MOND (modified newtonian dynamics) with relativity so as to provide another viable alternative. There's an article on this in NewScientist for 29 April, though I find that magazine has a penchant for pushing iconoclastic theories. See also here.
4. Inflationary cosmology and hypotheses about its antecedents. There are sound mathematical theories for such things, but little (for inflation) or nothing (for antecedents) in the way of physical evidence. The "standard" hypotheses is the Big Bang, but there are many variants and alternatives, associated with big names like Hawking, Steinhardt, Linde, Turok, etc. Unlike the previous examples, there's scant evidence, in spite of much elegant theory. Such theories need a category other than good/bad/wrong/ugly/not-even-wrong.
5. Quantum mechanics and determinism. Some quite reputable physicists keep trying to find some sort of determinism underlying QM. Most recently nobelist Gerard 't Hooft (NewScientist 5 May and here). Of course, this presents issues with the Conway/Kochen free will theorem. See here and here.
6. The Alvarez asteroid theory to explain the Cretaceous-Tertiary mass extinction. Since the discovery of the Chicxulub impact crater, people have become pretty convinced of this theory, despite heavy early skepticism. Yet evidence keeps turning up that the impact crater was formed long (ca. 300,000 years) before the extinctions began. See here.
There are many more examples, of course, including life sciences and medicine -- contentious stuff like megadose vitamin C, (denial of a relation between) AIDS & HIV, RNA-world, panspermia, etc. And that's without even getting into the squishy "sciences" like psychology, sociology, economics.
Having categories like good/bad/ugly may sometimes be helpful -- but they're definitely over-simplifications. Reality is messy.
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