In theory, a "podcast" is just a fancy way of saying "audio or video file made available on a regular basis". You don't have to have any special program to view them, most places either let you download it directly as file or have it streaming on their website. That's what I do.
The advantage of having a specially designed program to do it (or iTunes) is that it automatically downloads new content, so you don't have to go and find it yourself for each new episode. iTunes also has a nice database of podcasts, so you can browse. Ideo and PodNova are websites with this same functionality (database) but right in your browser, where you can also listen.
To the best of my knowledge, iPodder is the standard and/or best dedicated podcasting program, though their website is down, so a quick Google search brought up
Juice as a viable alternative. Also, if you have iTunes, that does the job as well, so you don't need to download any third party apps. I hear the new version of iTunes also has some features for uploading podcasts, though I can't comment first hand since I don't have it.
Also, you might want to download this video, it has a nice overview of how to
create podcasts.
http://revision3.com/systm/podcasting/media