I am a big fan of podcasts and big fan of the BBC, so you can imagine what I think of BBC podcasts.

My current roster consists of Arts and Ideas (Night Waves highlights), More or Less, and Analysis, in addition to the compelling Philosophy Bites (which is OU- rather than BBC-affiliated).

http://www.bbc.co.uk/programmes/p02pc9qx/episodes/downloads.rss

http://downloads.bbc.co.uk/podcasts/radio3/r3arts/rss.xml

http://downloads.bbc.co.uk/podcasts/radio4/moreorless/rss.xml

http://downloads.bbc.co.uk/podcasts/radio4/analysis/rss.xml

A trawl of the BBC podcast archive has also turned up the below, which I intend to add to that list.

http://downloads.bbc.co.uk/podcasts/radio4/r4sandel/rss.xml

http://downloads.bbc.co.uk/podcasts/worldservice/forum/rss.xml

http://downloads.bbc.co.uk/podcasts/5live/jot/rss.xml

http://downloads.bbc.co.uk/podcasts/worldservice/science/rss.xml

http://downloads.bbc.co.uk/podcasts/radio4/maths/rss.xml

http://downloads.bbc.co.uk/podcasts/radio4/iotp/rss.xml

http://downloads.bbc.co.uk/podcasts/radio4/iots/rss.xml

I use bashpodder http://lincgeek.org/bashpodder/, with a couple of slight tweaks.