This complete university course (from Fall 2007) on Ancient Greek History from Yale is the best history podcast I have found so far. It consists of 24 lectures of about an hour's length each, all given by Professor Donald Kagan. It starts with an introduction to Mycenaean Greece before moving onto the Greek Dark Ages and Homeric stories. The series ends with Philip of Macedon's victory at the Battle of Chaeronea and the Greek Polis' permanent loss of independence. Along the way it details all the major events including: the rise and strangeness of Sparta; the rise of Athens and democracy; Persian wars; and the slow decrease of power in the struggle for hegemony after the Peloponnesian War. Only the 27 years of the Peloponnesian War seem to be under represented in coverage (from my previous knowledge of history). Despite 4 lectures being dedicated to it in the syllabus, most of these are taken by finishing prior topics and the buildup to the war. For the war itself, Professor Kagan suggests looking to other sources as it it too much to cover properly, and instead talks in detail about two related topics - Pericles' strategy and Thucydides' history.
One thing I can't fault is the production. The podcasts are professional from start to finish. The only blemish is Professor Kagan's occasional coughing, but this is a minor issue. The podcasts are available in a number of formats on the course website: audio-only (the same mp3s that are on iTunes); video, in both high (around 700 MB) & medium (around 250 MB) bandwith forms; and, complete text transcripts. The website also includes the notes handed out with each lecture, although these unfortunately are without the original images due to copyright problems. The website itself is downloadable too (albeit with only links to the audio and video files). While videos of the lectures are available, it is not really necessary to download them as they mainly just show Kagan talking at his podium. Rarely does he use any visual aid during the lectures. Thus these are excellent podcasts to listen to audio-only - very little will be missed.
The lectures are often a recitation of events together with discussion of how and why things may have occurred that way (for instance a section on various military strategies and whether they were correct). The aim appears to be getting the listener into the mindset of the ancient Greek statesmen (and thus the citystates in general). A goal largely achieved to my mind. There is less discourse on daily life (but still some). Professor Kagan also talks a little about historical controversies and often compares ancient events to modern history (in particular around the use of military force). In both situations he tends to declare his own prejudices so the listener is not led too much.
This is a highly recommended lecture series - interesting content that goes into the subject with some depth and so well produced it is surprisingly easy listening.