Teach Yourself Books: These have a venerable history in the United Kingdom and figure prominently in my own personal history. Some decades ago they were practically the only available resource for many less common languages. I have bought over a score of these (and even read a few of them). Teach Yourself offers roughly 60 languages as well as other topics. These are probably the most traditional resource on this list. Each book offers a series of lessons, each of which typically consists of dialogs, vocabulary lists, some explanatory material, and some exercises. A "Teach Yourself Complete" course comes with a couple of CD's which may prove critically useful.
Strong points: Good for all-around learning, probably the best resource on this list for learning grammar.
Language/30 courses: 33 languages available. One course consists of 2 CDs plus a booklet (or the digital equivalent). The content is essentially like a phrase book, with a few basic vocabulary lists. There is no explanation of grammar, and only the scantiest introduction to non-Latin scripts (if relevant). As limited as these are, I have sometimes found them a useful first introduction to a language. And it doesn't hurt to commit a sizeable stock of standard phrases to memory.
Strong points: Good for pronunciation. The booklet provides a useful transcript.
Weak points: You won't learn grammar with these, unless you're extremely good at making inferences.
Pimsleur method: 50 languages available. I keep intending to do a separate post on this system. It is essentially an all-audio method. A full course consists of 30 half-hour lessons on CD (or the digital equivalent). The structure is simple: listen and say what they tell you to say. It is an easy ramp up into the language. Vocabulary and grammar are introduced gradually. Explanations of grammar are avoided as much as possible in favor of learning by imitation and repetition. The program also uses a spaced-repetition principle to maintain what you learn. Short courses are also available consisting of the first 10 lessons or whatever. For the more popular languages, as many as three courses are available (meaning 90 lessons). By the 90th lesson, you will have developed some nontrivial conversations skills.
Most courses have a smaller set of "reading lessons" that provide a basic introduction to the writing system. Unfortunately these are not closely connected to the audio lessons.
Strong points: Lots of speaking practice. Can be multitasked with walking, driving, etc. Helps develop an intuitive feel for the language.
Weak points: Could be so much better with a transcript. You may want to add a grammar resource.
Foreign Service Institute (FSI) courses. I want to mention these, although I have yet to try working with one. These were designed by the U.S. government for training diplomats. Many courses are available. The approach is traditional, generally comprising both a text and audio files. Since you pay taxes, you've already paid for them; i.e. they are copyright-free. Altruistic citizens have been digitizing and uploading these; see the preceding links. As of this writing, courses for 48 different languages are available; more may appear in the future.