Listen is a fantastic mobile podcasting client. I've set it up so that it downloads new episodes in the background when it's plugged into power and is connected to a wifi network.
In other words: It will automatically download new episodes during night so that I have fresh new episodes on my morning commute to school. It really shows what you can do with a phone-os that supports multitasking and downloading things in the background.
For more Android app recommendations visit my set: Android Applications.