What follows is merely my (Hartmut's) opinion: you may well find other German teachers who will denounce what you are about to read as the sort of ludicrous insanity that can only be cured by acupuncture or Gestalt therapy.  So please take this advice with a grain of salt!

• General Advice
• Size and Price
• Recommendations
• Warnings (i.e. I wouldn't buy these)
• Electronic Dictionaries

General Advice
Whatever dictionary you buy, you should absolutely do the following three things:

• Read the instructions in the front telling you how the dictionary is organized: how does it list plural forms?  How does it list irregular verbs?  How does it organize its entries?
• Once you have looked up a word in the German-English section, look it up in the English-German section (and vice-versa) to avoid misunderstandings.  Use the clues to the different senses of the word given in the dictionary--and use your common sense!  Then you won't find yourself saying "Dattel" when you mean a "date" on the weekend, or "Arbeitshose" for "overall" when you don't mean "work pants" :)  Note that in the German-English section, the clues to the various senses of the word tend to be in cryptic German, but they're still very much worth attending to if you have the time.
• Don't overuse the dictionary.  If you're trying to understand something, only look up words if you can't make a reasonable guess.  If you're trying to write or say something, consider first whether you could express your idea in a different way using the vocabulary you know before you look up a word or expression.  Puritan guilt culture may have conditioned you to look up every single word you're unsure of--but in fact, you should feel guilty if you do look up everything, because you'll learn less, lose sight of the overall picture, and learning German will feel like a chore instead of a pleasure.

Recommendations

• Webster's New World German Dictionary, Concise Edition (orange; roughly $14)  This is the dictionary I most recommend.  Don't buy the "Compact Edition": it's too small and not worth saving a few dollars.  Strengths: principal parts of irregular verbs (but not, unfortunately, present tense stem-changes) are listed in the verbs entry in the German-English section; typeface is very readable; organization is easy to follow; entries are well chosen and accurate.  Weaknesses: plural and genitive endings are only listed (in the German-English section) for words not following any regular pattern--but you can turn this into a strength by familiarizing yourself with the comprehensive list of noun ending patterns on page xvi, a very useful feature.
• If you're a beginner and not confident in your skills in navigating the abbreviations and conventions of most bilingual dictionaries, you may like the Harper Collins Beginner's German Dictionary, 2nd ed.  This contains a reasonable number of entries (but much fewer than the Webster's dictionary mentioned above), lots of helpful usage examples, and is especially easy to read and use.  It lists articles and plurals with every noun, and irregular verb forms with every verb. The ISBN is 0060748982.
• Any of the bigger dictionaries listing "Collins" and/or "Klett" on the publisher page are excellent: the above dictionary comes from that publisher. The "big" dictionary we recommend is the Harper Collins Unabridged German Dictionary.
• Despite the warning below, the bigger dictionaries from Langenscheidt's are quite good, and you might in particular consider buying the electronic version of their dictionary, Langenscheidt Collins e-Großwörterbuch Englisch from amazon.de or other online vendors. The "ASIN" number for this product is 3468909934 and it was published October 2004. The dictionary runs on the "PC-Bibliothek" platform, which also covers various dictionaries of the Duden (German orthography, thesaurus, etc.) and the Brockhaus (major German encyclopedia).

Warnings (i.e. I wouldn't buy these)

• Langenscheidt's dictionaries (the yellow ones)  These should be the best, because this publisher has a long tradition and publishes some great reference works.  Nevertheless, the compact Langenscheidt's dictionaries seem to me to be among the least useful and user-friendly dictionaries available.  But if you get a big Langenscheidt's dictionary and take the time to learn to use it, you will have a reliable and useful reference work.
  • Since writing this, I've gotten one email from someone who's very happy with his Langenscheidt's dictionary: Langenscheidts Taschenwoerterbuch, Revised Edition 1997--ISBN 3-468-11125-8

Electronic Dictionaries

The following information summarizes an email I received from an English teacher in Israel who is proficient in German:

• Most highly recommended: Franklin Deutsch-Englisch Professor PRO, BDS-1860. Offers 310,000 definitions (more than most paper dictionaries!), based on the Pons Wörterbuch für Schule und Studium. It supports the new German spelling but also accepts entries in the old spelling. The keyboard is QWERTZ and includes an "ß" key. Umlauts are filled in automatically, except in words like "schon" where the user is simply given a choice. It is also possible to type umlauts with a shift key. The BDS 1860 also includes an extensive grammar guide, including complete verb conjugations and noun declensions; you can input any form of a word and get the root and meaning in return. A Merriam-Webster English dictionary and an English thesaurus are shipped for free with the BDS 1860.
  • The instruction manual and box are all in German. Any user wishing to do so can download the entire English-language instruction manual from Franklin's website, or call Franklin's 800 number and ask them to send one for free. However, the help screens make the manual virtually unnecessary.
• Other Franklin products:
  • LDE-1660: Comparable to the BDS 1860, but based on Langenscheidt; the definitions seem to be less reliable than those given by the BDS 1860.
  • DBD-1660: also based on PONS
  • DBD-1450: based on PONS Compact; too small to be of any real use
  • SCD-1870-BL6: tiny display