Elementary
I'm afraid that I haven't find any podcast/audio recording which is suitable for students at this level. Sorry.
Lower-Intermediate
Big City Small World from the British Council
A podcast/audio series about a group of people. They talk about general life topics.
Intermediate
6 Minute English from the BBC
A long list of 6 minute podcasts/audio recordings on every type of topic. They are very good.
This is America from the Voice of America
Lots of podcasts on stories about America. It is good for listening to people with an American accent, but they do speak slowly. Some are a little boring though, so I personally don't use them too frequently.
Upper-Intermediate
Learn English Professionals from the British Council
Lots of short audio recordings/podcasts on professional, business and social topics. It is possible that some of them can be used with intermediate students as well.
Witness from the BBC
Interviews with people who witnessed important events in the world. They all last less than 10 minutes. There are thousands of episodes to listen to (five are released each week). Not all of them are appropriate for giving to students, but because there are so many, you will many which are.
These are the only podcasts/audio recordings here which haven't been designed for people learning English, but I have found them to be successful with my upper-intermediate students.
English in 10 minutes from Englishin10minutes.com
Podcasts from two English teachers where they either speak together on a subject (often on travel or different countries) or interview people. They are good for hearing both conversational English and different types of accents.
Advanced
At this level your students should be listening to podcasts or radio programmes (e.g. BBC World Service) designed for native speakers. You can use the Witness podcast (see above) with them or try to find something else.
To find something else for your students, take a look at the podcasts which are available from the BBC website and choose something which you think your students will find interesting or will be useful for them. I would suggest you pick podcasts which aren't long (anything over 20 minutes is excessive).