Good terminology, according to William Whewell, summarizes scientific progress, facilitates classification, and aids in accurate reasoning. It is perhaps fitting, then, that we owe a number of common terms, both in the sciences and about the sciences, to him. Here are some rough notes on the subject.
I. General Terms
Whewell is at least one of the first persons to use the word 'scientist' in essentially the sense we use today, in an 1834 review of Mary Somerville's On the Connexion of the Physical Sciences; he does not claim to have coined it himself, but is usually thought to have done so. He suggested it again, along with the word physicist, in 1840. The terms did not originally have wide acceptance; they first became common in American English due to various people like C. S. Peirce.
'Consilience' was Whewell's coinage to indicate the phenomenon of how a significant theoretical advance can make two apparently unrelated fields of knowledge "jump together" so that they can be given a unified account.
II. Terms Due to Whewell's Own Research
point of no tide
I once read a paper, I forget by whom, that said in passing that Whewell didn't do any scientific work himself; which is simply wrong. Setting aside the fact that Whewell would not agree with the view of science implied in the suggestion (for Whewell the effort to have good systems of notation and good terminologies is genuine scientific work, and essential to scientific progress, as is the effort to refine one's understanding of scientific methods), Whewell did a fair amount of scientific work in his lifetime, and his tendency to jump around from field to field was a common, although not universal, feature of the scientists of his day. The work which brought him the greatest honors in his day was his work on the theory of tides, which he wanted to bring under the umbrella of a mathematical theory. He failed at this, but it would be a mistake to consider his general work on the tides a failure. For one thing, it is in part due to Whewell that later scientists working on the topic had an idea of the complexity that they needed to take into account, and, for another, he ruled out a large number of false assumptions about the tides in the process (including Whewell's own original assumptions). But more importantly, he pioneered ways in which relevant data about the tides could be gathered and organized in useful form. One of his means of doing this was the cotidal map, which, following a suggestion that seems to have originated with Lubbock, used cotidal lines to indicate places on the globe that experienced high tide at the same time. He learned in the process that this is harder to do right than one might image, but a discovery made by Whewell in 1836 when looking at cotidal data was that there were points in the ocean that were, in effect, always at high tide (an effect visible on cotidal maps -- in Whewell's case, on the cotidal map of the North Sea); this was confirmed in 1840. Whewell's own term for this was simply 'point of no-tide', which is occasionally used even today. The more usual term nowadays, however, is 'amphidromic point', which was coined later by Rollin Harris.
III. Physical Terms
Whewell proposed these to Faraday in 1834. One of Faraday's and Whewell's big concerns in developing the terminology was to come up with a fairly intuitive terminology, which all of these would be to someone who, unlike Faraday, had a solid knowledge of Greek, but one that at the same time would not imply a particular theory of how they worked.
IV. Geological Terms
William Whewell suggested these terms to Lyell in 1831; Lyell had asked Whewell to help him refine terms he was using for geological epochs, and Whewell responded by giving him several suggestions, of which these, added in a postscript, were the ones Lyell decided to use. A major concern for Whewell and Lyell was, as Whewell said, the fact that in scientific matters definition is rarely what you want words for; you usually want them instead to classify.
Whewell seems to have coined these terms in a review of Lyell's Principles of Geology.
O as the symbol for oxygen
It seems like a minor one, doesn't it? But one of the major scientific disputes in which Whewell was involved was the dispute over the best notation for chemistry, a topic on which there was considerable confusion and disarray at the time, since different chemists used different notations. Setting aside Dalton's symbolic representations, the most important notation system prior to Whewell was that of Berzelius, in which oxygen was represented by dots. Whewell campaigned very strongly for a more purely algebraic system of notation than is found in Berzelian systems, although he was willing to bend some features for practical convenience; one of his extraordinarily and, to us, surprisingly controversial proposals along these lines was his suggestion in 1831 that the letter O be used to indicate oxygen instead of the dots. One of the reasons people were so attached to the dots is that they were seen as neater and more clear than letter O, which increased the need for brackets and parentheses. In any case, the disputes over chemical notation had a long history after the dispute between the Berzelians and the Whewellians, but modern notation has features derived from both.
The Whewell equation is a formula for describing a plane curve without requiring a particular coordinate system. Whewell proposed a version of it in a paper in 1849; hence the name.
While not coined by Whewell, it is perhaps appropriate, given his extensive mineralogical work that there is a mineral named after him. Whewellite is CaC2O4·H2O, i.e., calcium oxalate monohydrate. As far as I can determine, the name seems to be due to its discoverer, Henry James Brooke; Brooke had already discovered a mineral, which came to be called brookite, and the decision seems to have been made to name it after Whewell to avoid the unseemly situation of two minerals named after one person. At least, this is the reason that seems to be given in most mineral handbooks; how accurate it is, I do not know.
Whewell also has a crater on the Moon named after him.