There are a few podcasts I tend to listen to as I have time. Since I work with a wide range of technologies, I've tried to group them together into a semblance of order. There are a few others I am evaluating, but since I haven't listened to a large enough body of work, I'll refrain from listing them at this time. If there's one you think is particularly valuable or interesting that I don't have listed, please leave it in the comments.
.NET Rocks - http://www.dotnetrocks.com/
This is one of the best done podcasts out there and they cover anything and everything related to Microsoft .NET. That's a broad brush of most anything that interacts with Microsoft technologies. This one runs twice a week and is about an hour each podcast, but if you can spare the time, it's worth the listen.
Plumbers @ Work - http://plumbersatwork.com/
These guys from Canada talk about a lot of different things, but most of it relates to .NET. They were quite for a while but then popped up two episodes in February and March. Another one I'm hoping gets more active again soon.
ARCast used to be hosted by Ron Jacobs and covers architecture. While the focus is mostly on application architecture, there were some times when infrastructure architecture was covered. Unfortunately, this podcast has been on hiatus since the end of the year when Ron Jacobs moved on to another opportunity in Microsoft.
General Technology (Microsoft)
Behind the Code - http://channel9.msdn.com/shows/Behind_The_Code
Behind the Code talks to the people behind the technologies, and it's extremely interesting to hear the folks who have developed the things we use every day explain their challenges and ideas in their own words.
Going Deep - http://channel9.msdn.com/shows/Going_Deep
As the name implies, Going Deep is where folks do a deep dive on the technologies they are/were involved in. If you are interested in the Why? question, this is a great podcast.
RunAs Radio - http://www.runasradio.com/
As .NET Rocks is for the developer, RunAs Radio is for the infrastructure folks. It was spun off from .NET Rocks and is a weekly, half-hour show. Same quality as .NET Rocks and it shares some of the same people. If you work in IT infrastructure (in Microsoft or related technologies), this podcast should be right up your alley.
TechNet Radio - http://technet.microsoft.com/en-us/bb510143.aspx
Not sure why the folks at Microsoft don't have a more friendly link, but "it is what it is." This weekly podcast covers some aspect of Microsoft technology, usually whatever is "new" and "fresh."
A podcast which focuses on MySQL. This one has also been quiet for a few months, but hopefully it'll pick back up again soon.
SQL Down Under - http://www.sqldownunder.com/
As the name implies, a podcast for SQL Server out of Australia. It's hosted by Regional Director and MVP Greg Low and the episodes typically have an extensive interview with a luminary in the SQL Server or general database category. It's not all technology stuff, either. For instance, the podcast with Kevin Kline talked a bit about family and the balance between life and work.
The Voice of the DBA - http://sqlservercentral.mevio.com/
This one is done by SQL Server MVP Steve Jones and it comes out every weekday. These generally tend to be short, they're not always on SQL Server, but as is standard Steve Jones' style, they make you think. This one is an easy one to stay up to date with and it's well worth the few minutes every day spent watching.