Keith Devlin (British-born author of a number of interesting, well-written and highly recommended books) gives a 5-minute interview on NPR (a US radio station) about infinite numbers such as cardinal numbers like You can find the interview at A Finite Discussion of Infinite Numbers
Simon Singh did a couple of series of short programmes about numbers on the BBC in March 2002 and October 2003. You can listen to his discussion of Infinity; there are links there to the other broadcasts as well as to other Science programmes. Worth listening to.
Some(6,7,8,9??) years ago there was a BBC radio series on the history of mathematics which was had me rolling about as it was so (intentionally) funny. Anyone remember it or know if it is available anywhere?