What are the best English dictionaries, word histories, idiom dictionaries, grammar guides, usage guides, style guides, and so on?
That would depend entirely on what your needs are, IMO.
Personally, I’d go for Chambers 20th Century Dictionary (although I see the current edition is called Chambers Dictionary, 11th edition),
Roget’s Thesaurus (although I prefer the format older editions were in) and
Brewers Dictionary of Phrase and Fable…
But that’s just me; as Exapno says, it depends, and there are an awful lot of them out there!
As a student of English I love me some good Oxfords and Cambridges. 
Have Cambridge Idioms as well as Phrasal Verbs and both were very helpful and easy to use.
You can also pry my Oxford Collocations from my cold, dead, ink-stained fingers. That one I would easily recommend for a native speaker who sometimes can’t find the right word or doesn’t want to repeat themselves. It has the added advantage over any thesaurus I’ve seen that you look up the context, and then find a suitable word.
I also have a very interesting VISUAL dictionary from DK (as seen on their website http://us.dk.com/nf/Book/BookDisplay/0,,9780756626068,00.html?strSrchSql=dictionary+visual/Ultimate_Visual_Dictionary_DK_Publishing#), you can learn names of parts of machines you never even thought about.
If you have some money burning a hole in your pocket you can spring for the complete OED. That’s one dictionary that gives a thorough history of words, apart from an exhaustive description of present usage.
OK, I’ll just stop plugging Oxford now.
I found out about my favorite English usage guide when David Foster Wallace died. I was looking for essays of his on the web and found his review of A Dictionary of Modern American Usage, by Bryan A. Garner. The essay, which is much more than a book review, prompted me to buy a used copy of the book online. I ended up reading it cover to cover, which I don’t think I had never done with a reference book before. It is a well-written and well-researched book, with citations from published sources for everything.
Well, the best English Dictionary (and probably the best in any language) is the Oxford English Dictionary, but that’s usually overkill for what most people want to do.
The standard style guide for book publishing is the Chicago Manual of Style; for newspapers, it’s the AP Style Guide, and for government (and many other uses), it’s the GPO Style Manual. There’s also Karen Elizabeth Gordon’s The Transitive Vampire and The Well Tempered Sentence, which are not only great guide, but also a hoot to read.
Avoid at all costs Lynn Truss’s Eats Shoots and Leaves. Leaving aside the fact that she knows next to nothing about the language other than her own unfounded prejudices, it’s completely useless as a guide because it’s impossible to look up a particular rule without rereading the entire chapter.
I second RealityChuck’s nomination for the works of Karen Elizabeth Gordon. I caution that The Disheveled Dictionary is not really of value; it’s kind of fun, but not a reference.
Strunk & White’s Elements of Style. You can’t go wrong with the classics.
I have a copy at home in paperback, and recently saw a hard cover in my local bookstore. It’s such a slim, sleek thing that I don’t need, but oh, I want.
The Bedford Handbook by Diana Hacker is the gold standard, IMO, as a grammar and composition handbook.
Your Own Words by Barbara Wallraff is a good guide to reference books (dictionaries, style guides, etc.).
Writing with Style: Conversations on the Art of Writing, by John Trimble.
It’s a clear, easy, enjoyable read that will improve your writing.
- For grammar usage: Harbrace College Handbook I have the Eleventh Edition, published in 1990. I’m certain that there have been more recent editions. It is a guide for writers, but it can also be used as a textbook in course work. I consider it the standard for settling disputes on grammar usage.
I began college with the Fourth Edition and it got me through a top school and into careers in publishing, writing, and teaching English.
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Writing style: The Elements of Style by Strunk and White Like a small book of wisdom for writers
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Dictionary: The OED (Oxford English Dictionary) Priceless for the information it gives on word origins!
On the other hand, just think about what Exapno Mapcase posted.
Go back and read some of Exapno Mapcase’s posts and ask yourself what makes them so good.
Seconded for truth. This was actually a required text for an engineering class back when I was in school - I guess the professor (rightly) assumed we engineers needed some writing lessons. I really enjoyed reading the book just for fun.
I still chuckle when I think of “Soulwise, these are trying times.”