Podcast.de
Podcast.de has pretty much everything and it is a good starting point. I don't like the website, though. It is a bit quirky and sometimes slow.
WDR video podcasts
Some favorites:
Die Sendung mit der Maus
Excellent for intermediate students and advanced beginners.
Quarks & Co
Kopfball
Tagesschau - news
Computerclub2 Computers - very popular.
Radiotatort - Krimis
SWR2 Wissen
GEO audio
WDR radio podcasts
Click on individual radio stations to get a list of podcasts.
Favorites
sonntagsfragen
Erlebtegeschichten
leonardo
klartext
philosophischesradio
I wouldn't worry about the title. Some excellent stuff here.
politikum
essenundtrinken
presseclub
leonardo_darwin
Zeitzeichen
wdr2kompakt
WDR 5 Bücher
Radioquarks
fhgespraeche
hallouewagen
comedy
Merkels Mailbox
Schlaflos in München
Slow German
BR podcasts
Children's podcasts
Die Sendung mit der Maus
Klicker - Nachrichten für Kinder
Käpt'n Blaubär
It's very...German.
Lilipuz
Baerenbude
For very small children.