The best resources are at the top of each section.
Dictionaries
Kanji Grammar
Beginner's
Lessons Advanced
Lessons Odds and Sundries
So where do I begin... learning Japanese?
learning
to read Japanese? learning
otaku Japanese?
The state of Japanese-English dictionaries is a sad and sorry one indeed. The kanji dictionaries are excellent--but they don't list words which are written in kana. The dictionaries which list words in both kanji and kana tend to be geared toward beginners. And neither of these have much in the way of slang.
Into this void comes the Japanese <-> English Dictionary Server, an online database with kanji, kana, slang, names, technical jargon, and about eighty different ways to show the results. (This is important if your computer isn't set up to display Japanese.) The dictionary even includes idiomatic phrases, though they're run together with no spaces between the words (so hotoke no kao mo sando, "to try the patience of a saint," appears as "hotokenokaomosando"). And to gild the lily, the site loads quickly and is rarely down.
A few of the definitions in the Japanese <-> English Dictionary Server are a little eccentric, which brings up another point: No matter what resource you use, cross-check it with another. Japanese is enough unlike English that dictionaries contradict one another all the time. Often it's a matter of the tone or feel of the word, and each reference takes a different slant. Cross-checking will keep you from making some truly embarrassing mistakes.
These are some other good dictionaries:
Random House's Japanese-English English-Japanese Dictionary by Seigo Nakao. One of the best kanji-and-kana dictionaries out there.
The Living Language Common Usage Dictionary. Surprisingly in-depth for a small dictionary. Using this and the Random House Japanese-English English-Japanese Dictionary will get you just about any common or semi-common word you'll need. It often has a different take on words than the Random House dictionary, so cross-check them frequently.
A few simple online dictionaries:
Kanji
The Japanese <-> English Dictionary Server has a searchable Kanji database of over 6000 kanji.
Dom's Kanji Tattoo Archive is, as it says, a guide to Japanese symbols and characters and their meaning, intended for people using them for tattoos. (You can also use it to read those kanji-emblazoned baseball caps I see nowadays. Some of you are walking around with black caps embroidered with a funky, complicated red kanji which would make you look much cooler if it didn't mean "leg." Don't lie to me, I saw you at Mardi Gras.)
Kanji & Kana: A Handbook of the Japanese Writing System, by Hadamitzky and Spahn, is an excellent learning guide and a good resource for looking up kanji in the absence of anything else.
All of the major Japanese-textbook publishers (Kodansha, Tuttle, et al) have put out decent kanji dictionaries. I haven't used any of these, so I couldn't say which is best. They all have fans.
Grammar
Essential Japanese Grammar, by Everett F. Bleiler, published by Dover, is an excellent whirlwind tour of basic Japanese grammar.
Japanese Verbs and Essentials of Grammar by Rita L. Lampkin, published by Passport Books, has an extensive section on... well, damn near everything. But the main strength of this book is the section on verb and adjective endings, in which Lampkin systematically explains not only the basic endings, but the more advanced endings which most books touch on only in passing. Extremely useful for translating.
The Quick and Dirty Guide to Japanese, by Tad Perry, is a fast-and-furious walkthrough of Japanese.
All About Particles explains not only grammatical particles, but sentence endings as well.
Beginner's Lessons
There are a number of teach-yourself-Japanese courses on the market, most notably Japanese for Busy People.
Tumbleweed's Resources for Learning Japanese has everything from beginner's tricks for learning Japanese to grammar articles for intermediate students. The links are excellent but partly defunct.
Easy Web Japanese is a set of very basic exercises and culture notes.
Intermediate Lessons
Tumbleweed's Resources for Learning Japanese has everything from beginner's tricks for learning Japanese to grammar articles for intermediate students. The links are excellent but partly defunct.
Advanced
Lessons
Odds and Sundries
Kinki Japanese: The Dialects and Culture of the Kansai Region by Palter and Horiuchi, published by Tuttle.
Japanese Street Slang by Peter Constantine, published by Tengu Books, is the only Japanese slang reference published in English, apart from several other books which Constantine based on this one. Some reviewers panned it as vulgar, filthy, and—most damning—outdated, but it's what there is.
Minimum Essential Politeness by Agnes M. Niyekawa, published by Kodansha, is a guide to ultrapolite Japanese. (It's actually called respect language or keigo.)
For Otaku Only
Yuu Yuu Hakusho Doujinshis in English has a fabulous dictionary of anime words and Japanese sound effects. YYH Dj's in English is a yaoi (male-male) site, so be prepared to be sidetracked.
Japanese for Anime Lovers - words, phrases, and simple grammar, taught with quotes from Magic Knights Rayearth.
The 100 Most Essential Words in Anime - This list explains the connotations of (well over 100) words as well as their basic meanings.
used mainly by women
used mainly by men