These texts move away from a traditional grammar-translation approach and focus more on reading and aquiring the language. The approaches are fairly disparate, but all of them, as far as I can tell, apply techniques for modern languages to teaching ancient Greek.
- Paula Saffire and Catherine Freis. Ancient Greek Alive.
- Günther Zuntz. Griechischer Lehrgang (German and Greek. There is apparently an English version which is recommended by Seamus MacDonald)
- Athenaze (Italian edition, adapted by Luigi Miraglia to resemble Orberg's Lingua Latina. It is available at his website)
- Polis Koine. A relatively new French-based course which aims to teach Ancient Greek as a living language (website)
- Assimil's Le grec ancien sans peine. Sample page here.
- A number of people have also suggested the Greek Ollendorff by Asahel Clark Kendrick. Although it's a traditional grammar-based course in many ways, it includes a lot of practice exercises, often in the form of dialogues.
- W. H. D. Rouse. A Greek Boy at Home. (Meant to accompany his First Greek Course. Files for both are here. He also published a reader, available here)
- C. W. Peckett and A.R. Munday. Thrasymachus.
- Joint Association of Classical Teachers. Reading Greek.
- C.E. Freeman. A Greek Reader for Schools (reprint isbn 0865162670)
- Adolf Kaegi. Greek Readings for Review (reprint isbn 0865165491)
- Francis David Morice. Easy Stories in Attic Greek (updated by Anne Mahoney, isbn 1585101893)
- Evelyn Abbott. Easy Greek Reader.
- Frederic Jacobs. The Greek Reader.
- William George Rushbrooke. A First Greek Reader.
- John E. B. Mayor. First Greek Reader.
- Archibald Hamilton Bryce. First Greek Reader.
- Charles Melville Moss. A First Greek Reader.
- Alexander Waugh Young. A Tutorial Greek Reader.
- Albert Harkness. First Greek Book. (The third part of this text includes reading selections)
- John Stuart Blackie. Greek and English Dialogues.
Johannides' book is hilarous, but unfortunately printed in the verdammt German Fraktur. I'm not sure whether Sellner's book is a phrase book or more of a collection of sententia antiquae.
- Alfred Sellner. Altgriechisch im Alltag
- E. Johannides. (pseud of Eduard Johnson. biographical note here) Sprechen Sie Attisch?
Vocabulary grouped around semantic fields.
- H.W. Auden. Greek Prose Phrase-Book
- J.H. Schmidt. Synonymik der griechischen Sprache (4 volumes, available on googlebooks)
- Pillon and Arnold. Handbook of Greek Synonymes.
- Robert Weir. Greek Vocabulary for Young Boys
Two titles also look useful, but I'm not sure how much they're oriented to the reader who knows Greek, and how much they're intended for students interested primarily in the philosophical concepts.
- Francis Edward Peters. Greek Philosophical Terms.
- J. O. Urmson. The Greek Philosophical Vocabulary.
These books are primarily useful for vocab drilling and are organized alphabetically or according to frequency in Greek texts
- Malcolm Campbell. Classical Greek Prose: A Basic Vocabulary
- W.J Bullick and J.A. Harrison. Greek Vocabulary and Idiom
- Owen and Goodspeed. Homeric Vocabularies
- Thomas Meyer and Hermann Steinthal. Grund- und Aufbauwortschatz Griechisch
- Menge-Güthling Griechisch-deutsches und deutsch-griechishes und Wörterbuch
- G. M. Edwards. An English-Greek Lexicon
- S.C. Woodhouse. English-Greek Dictionary
- J. Jackson. Iambica