PodcastRE

PodcastRE offers metadata information and connections to more than 150,000 distinct audio files from more than 1000 distinct podcast sources.

Listen Notes: The Best Podcast Search Engine

The greatest podcast search engine and database is called Listen Notes, and it offers both a developer-facing API and a user-facing website.

SoundCloud

SoundCloud is an internet-based platform for sharing music and distributing audio files.

University of Oxford: Podcasts

A compilation of videos produced by Oxford University.