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.
Upper-Intermediate
Witness from the BBC
Interviews with people who witnessed important events in the world. They all last less than 10 minutes. These podcasts/audio recordings haven't been designed for people learning English, but my upper-intermediate students regularly use them and don't find most of them too difficult.
Learn English Professionals from the British Council
Lots of short audio recordings/podcasts on professional, business and social topics.
English in 10 minutes from Englishin10minutes.com
Podcasts from two English teachers where they either speak together on a subject or interview people. They are good for hearing both conversational English and different types of accents.
Advanced
At this level you should be listening to podcasts or radio programmes (e.g. BBC World Service) designed for native speakers. You can use the Witness podcasts (see above) or try to find something on a topic you are interested in.
To find something else, take a look at the podcasts which are available from the BBC website and choose something which you find interesting or will be useful for you. If the podcast is too difficult (or too easy), try listening to another. You will eventually find something which is right for you.
Two podcasts that you may find interesting from the BBC are From Our Own Correspondent and Thinking Allowed. In each episode of the 'From Our Own Correspondent' series, five BBC journalists from around the world talk for five minutes each about things which they have seen. While the eposodes in 'Thinking Allowed' talk about things that affect people and society (from cooking to crime). Both are very interesting and in them you'll hear advanced vocabulary on a variety of different topics. These podcasts are longer than the others (around 27 minutes), but you can always pause them when you want.