After a certain point, probably a few years into your study, depending on your motivation and environment, you will reach a point where you will need full-speed, native level listening practice. I had searched on and off over the years for something that would do this, and settled, most times, for Japanese dramas and comedy (Gaki No Tsukai,, Gaki Files)
Recently, however, I have finally put two and two together and began to use my iPhone to listen to Japanese on the go. There are two ways to do this that I have found. One is to explore the world of Japanese podcasts!
This is made super easy if your account is directly connected to the Japanese iTunes store. If so, just open up iTunes, click this iTunes store on the left, and then podcasts on the top bar and viola. I would recommend the talkshow or internet radio podcasts. They can be very topical to events in Japan, but provide a nice slice of life and insight into Japan.
Another option is to listen to internet radio directly on your iDevice using Ootunes. Ootunes has access to thousands upon thousands of internet radio stations from all over the world, including Japan. Most of these stations are in fact music (and many are very anime-themed stations), but a few are talk shows.
The great thing about this is that you can freely switch between stations without having to connect the device back up to iTunes to download more. You will need an active connection to the internet, though, and your experience may change depending on how good your data connection or plan is.
As a last note, I will recommend Nihongo Juku, a site long abandoned, but it does offer some awesome listening activities. It has full scripts and lists of difficult words. This is great for intermediate learners.
Do you have any other tips for practicing your listening?
UPDATE 26/April Beginners may want to try out this website!
UPDATE 03/July: A few more recommendations for Podcasts: (via Reddit)
SBS Japanese Podcast - Professional audio clips you can download individually.
Jesus Lifehouse - Bilingual Christian Podcast
Stand By! - A high-level news discussion program
Bananaman no Bananamuun - Famous comedy duo
Shinya no Bakachikara - Stand-up style comedy
Eiga Daisuki - While it has been discontinued, offers movie discussion in Japanese
Nukisashi Naranaito - Comedy duo
Social Subjects Talk Radio - All in the name, really