As someone who spends a lot of time listening to podcasts I'll rattle off a few I've found to be very enjoyable.
Eurotrash Security Podcast
Probably my favourite podcast as it's European albeit a bit light on technical content. News and chat based mainly. They cover a lot of the conferences which is good if you can't get to many (like me). The European slant on the news is particularly good as there is quite a difference between US data privacy law and European so often there are considerations which don't get covered on the other podcasts I'll now list.
I also enjoy their MicroTrash podcasts. Short interviews with people, typically regarding their talks at conferences.
Pauldotcom Security Weekly
Almost the de facto security podcast. Despite the advertising and the stick they get for being corporate I still rate this as just about the best podcast all round (if it weren't for my European bias it would be my favourite). The show provides regular segments of news, interviews and technical stuff. Lots of in jokes so I suggest you download the back catalogue (I did, took me about six months to get through it, they've been going five years).
What can you say about this one? If you're looking for pound-for-pound security content then EL is perhaps a bit lighter than the others but what you do get is the unique view of the world shared by Chris Nickerson and Ryan Jones. Be prepared for lots of swearing, outrageous, completely inappropriate jokes that will leave you crying with laughter in the car (or wherever you listen) grateful that no-one knows what you were laughing at. You're going to hell if you listen. ;-)
In between the laughs what you will get is straight-talking, no nonsense opinion on the state of information security today. Chris and Ryan's qualification to discuss security is beyond question (for me anyway) and sometimes you can learn an awful lot from a throw-away comment from one of those guys. They get your brain thinking about security in the right way imho. Nickerson focuses on security from a perspective of business impact. CEO's don't care if you got "root". They do care if you got their data.
Social Engineer Podcast
This is another excellent podcast focused, as you might imagine from the name, on the human element of security. The guys behind it include Muts and Chris from Offensive Security (think BackTrack) and Rel1k (Dave Kennedy) who wrote the Social Engineering Toolkit (SET).
The thing I like about it is they have a guest interview each month who is nothing to do with security, typically. They try to interview people who use social engineering skills, such as framing, micro-expressions or plain acting, in their day-to-day jobs in order to get a much broader view of the world of human manipulation. If you enjoy human psychology like me it's fascinating.
Southern Fried Security Podcast
Only listened to a couple of episodes of this but I enjoyed the short, news focused format. They tend to keep it to half an hour.
Infosec Daily Podcast
Literally it's daily. I've got a massive stack to listen to and again, I've only managed to listen to a couple but again, the guys behind it are well regarded in the industry so got to be worth a listen.
Security Justice is also supposed to be good although I've not listened to any of those yet. This is co-hosted by Jack Daniel, someone again who is well regarded in the industry.
All of these are easy to find in iTunes, if I can work out how to extract a link from iTunes to each I'll try and post them on here later.