After a certain level of mastery I've found that most language courses, even those intended for advanced students, simply are not useful anymore. Instead, I have collected a number of more specialized resources which I have found helpful (whether my German has actually improved as a result is of course more difficult to evaluate)
1. A good monolingual German dictionary. Duden and Wahrig are the two standard options; I prefer Wahrig, as it tends to have more examples, but a medium-weight copy of either is adequate for most purposes.
This is absolutely crucial for more advanced study, in my opinion, as a bilingual dictionary simply doesn't provide the necessary information on usage. Furthermore, a monolingual dictionary is a useful way to learn synonyms and other equivalent expressions. (Keep the bilingual dictionary on hand, however: there are still some occasions where it is invaluable -- such as for checking the names of things like tools or plants, or where you don't know the meaning of the words used to define it.)
Duden also produces a number of other specialized dictionaries, but in general I haven't found them to offer much that a regular dictionary wouldn't. However, there is one exception: a Fremdwörterbuch is worth getting, as German dictionaries frequently do not include words which are of obviously non-German origin, even when these words have become fairly well established in the language.
2. An advanced reference grammar. There are many nuances of usage which are simply not generally taught in grammar courses. I like Lederer's A Reference Grammar of the German Language and Hentschel & Weydt's Handbuch der deutschen Grammatik. Both of these are modern descriptive grammars which make use of contemporary linguistic theories of syntax. Lederer's book is specifically oriented towards the needs of English-speaking learners; Hentschel and Weydt's is not.
3. Synonyms, idioms, and usage.
These books are intended for students at a variety of levels. An intermediate student will find them useful for expanding his understanding; a more advanced student will return to them for fine-tuning his knowledge.
Unlike the other books, which focus on the finer points of usage and distinctions between related words, Hachenburger & Jackson's text is intended for vocabulary building. Its thematic arrangement of topics is useful for students who, like me, have fairly advanced knowledge in some areas (literature) but are rather lacking in others (politics, economics). The book includes complex expressions in addition to more basic vocabulary.
R.B. Farrell. A Dictionary of German Synonyms.
K. B. Beaton. A Practical Dictionary of German Usage.
Martin Durrell. Using German: A Guide to Contemporary Usage
Sarah M. B. Fagan. Using German Vocabulary.
Bruce Donaldson. Mastering German Vocabulary: A Practical Guide to Troublesome Words.
Petra Hachenburger and Paul Jackson. Topics, Questions, Keywords
These two books are the closest thing I have found to a true text-based course for advanced students. The exercises are challenging and require not just a high level of comprehension, but also mastery of the usage of various compound forms and fixed expressions.
Joachim Buscha. Deutsches Übungsbuch. (Reprinted, I think, in revised form as Übungsgrammatik Deutsch)
Günter Schade. Einführung in die deutsche Sprache der Wissenschaften.
German figures of speech are one thing I have definitely not yet mastered. For finding equivalents to English expressions, something like Peter Lupson's Guide to German Idioms, or Henry Strutz's German Idioms, which contain indexes for keywords in both languages, is invaluable.
The online, searchable Redensarten-Index is also quite useful. (Since this is not a bilingual database, it does require that one has at least a general idea of which keywords are involved in the German expression being sought.)
Additional online collections of idioms and sayings include redensarten.net (searchable by theme) and Phraseo.
And last but not least, Phrasen.com is a bilingual (English and German) collection of phrases ranging from quotations and conventional sayings to everyday collocations. Content is at least partially user-generated, and there is a form for entering translations of phrases or ones which you wish have translated.
4. Specialized Vocabulary
Although I generally try to avoid actively translating when using a foreign language, in more specialized areas I've found that there is no replacement for a bilingual glossary for looking up terms which one already knows in one's native language. Many fields of science and industry have printed dictionaries in two (or more) languages. For the humanities a bit more searching is necessary.
Literary Theory & Criticism
Saad Elkhadem. The York Dictionary of English-French-German-Spanish Literary Terms
W.V Ruttkowski and R.E. Blake. Literaturwörterbuch: in Deutsch, Englisch und Französisch
Rose M. Bachem Alent. Companion to Foreign Language Composition: A German-English Guidebook to Literary Terms
E.W. Herd and August Obermeyer. A Glossary of German Literary Terms
Alent's text is less a glossary of specialized terminology than a collection of thematically arranged vocabulary and phrases (both basic and more advanced) useful for discussing literature in general. The advantage to this book is that it includes information such as gender of nouns which a non-native speaker needs when using the vocabulary. The other glossaries generally do not include this information, which is highly irritating.
Herd & Obermeyer's book has a somewhat hybrid character. It is organized like an ordinary dictionary of literary terms, but the headwords are all in German while the explanations are in English. It is somewhat in need of updating (I would have liked to see terms for more recent trends in German literature, such as Trümmerliteratur or Wenderoman).
I've managed to track down several online sources which include English-German glossaries of sewing terminology (if I ever have time it would probably make sense to compile them into a single list). Unfortunately, there are still gaps and I find myself spending way more time than necessary simply trying to figure out what a particular notion or type of fabric is called so that I can then figure out where to purchase it.
I also recommend Pons' Bildwörterbuch for more detailed information about all kinds of everyday objects. My voabulary for things tends to be highly generic (I can talk about sinks, beds, and doors, but not drains, bedsprings, or door frames), and sometimes -- for example, when something isn't working the way it's supposed to -- that's not enough.
5. Slang, Colloquialisms, Neologisms
There are a couple of good sites for looking up colloquialisms that often haven't made it into the dictionary:
The Deutsche Welle podcasts Wort der Woche and Sprachbar also contain some interesting tidbits on idioms and colloquial language, although in general the podcasts are aimed at a beginning-intermediate audience.