Here are some of the best:
This American Life
Produced by Chicago Public Media, This American Life is a hugely successful radio program on NPR that brings its audience amazing stories based around a specific theme every week.
Memorable episodes include: Act V and Middle School. Leaving Cert Students might be especially interested in a recent episode entitled 'How I Got into College'. Act 2's amazing story about a Bosnian refugee Emir Kamenica is mind-blowing.
For those with an interest in Science or just fascinated by the world around us RadioLab is a treasure trove of mad facts and gripping stories.
Episodes include: the Bad Show and What a Slinky Knows.
BBC Radio 4
There are mountains of great stuff available from BBC Radio 4 from documentaries to drama to great comedy...Find some funny here.
Let me know if you've found any other great radio podcasts out there and enjoy :)