Some books and resources I've found helpful when doing German tutoring.
The textbook I generally recommend for self-study is Deutsche Sprachlehre für Ausländer by Dora Schulz and Heinz Griesbach. This is a natural-method textbook (i.e., all explanations are in German) which starts out with easy readings and dialogues that get gradually more difficult, and it contains plenty of grammar drills (making questions out of statements, replacing nouns with pronouns, and so forth).
The other books I would recommend are the Living Language Ultimate Course and Teach Yourself German, as both these series are generally fairly solid, reasonably priced, and include audio tapes for practice. The usual problem here is a tendency to be a bit superficial - although they go beyond the tourist phrase-book level - and a lack of sufficient practice exercises. But both series serve as a good starting point.
I have generally found reading/grammar-based courses to meet my learning style the best. "Listen and repeat" type courses such as Pimsleur drive me nuts, and textbooks intended for classroom instruction are not necessarily useful for the independent learner (plus, they are frequently incredibly expensive).
There are tons of resources for learning German online; unfortunately, I haven't done extensive research on this as I haven't any immediate need for beginning German instruction. There does seem to be a gap in most languages between phrase-book type stuff and advanced dialogues; most podcasts are more suitable for intermediate/advanced students who already have a good grasp of the basics and need practice listening and building vocabulary.
The online Beginners' German course by Paul Joyce looks good, although I haven't used it with students. It includes a fair amount of audio.
The German radio Deutsche Welle has audio resources for learners of all levels.
The BBC also some lessons in basic German. My impression is that it provides more than just a phrase-book, but is probably not enough for someone who seriously wants to learn the language.
Both these readers are intended for beginners:
Hannelore and William Crossgrove. Graded German Reader. ISBN 0669201596
Heinz Thorn. Beginner's German Reader. ISBN 084422170
Kaleidoskop has short readings on various topics on everyday life in Germany. Seems to be oriented more towards a school-age audience, but many of the topics in the should be appropriate for learners of all ages. Beginners should check out the archive, which is sorted by topic.
Worksheets provided by Nancy Thuleen to accompany her introductory German courses.
german-grammar.de provides a good overview of essential grammatical topics, as well as some discussions of more advanced issues. Includes audio of all examples. Quite well done, although probably not suited for use as a stand-alone course because of the lack of exercises.
Fundamentals of German. Paradigms and grammar from the University of Houston.
Deutsche Grammatik online has exercises and games on various grammar topics (primarily level B1 - intermediate - and above)
Blogs for beginning and intermediate German language learners:
transparent.com's German blog includes essays on various topics related to German language and culture. The posts are sprinkled throughout with relevant vocabulary, so it's a good way for a beginner to pick up some new words.
Deut(sch)lich includes mini-lessons for learners of various levels. The blog is entirely in German, but there's some material that should still be useful for a beginner (these are listed under the tag "A1").
pukkagerman is a podcast aimed at beginning to intermediate German learners. All episodes include a complete transcript and translations of vocabulary words.
Audio Lingua has audio files of varying difficulties in German (also in various other European languages); sortable by level.
Slow German offers podcasts (with transcript) about German culture and life in Germany.
German Words Explained are short podcasts in German focusing on key words from German politics, culture, and media.