Skype (now owned by Microsoft) is a great way to study Japanese. Skype is popular around the world, as it combines Internet video calling, traditional phone calls, and text chat.
Though you can use Skype to call real phones from your computer (handy if you're in Japan or if you have friends in Japan-- I use it myself to call home for $0.02/minute), the real highlight is that you can make computer-to-computer calls free. All you need is a microphone or headset, readily available at major electronics stores (or built-in if you have a Mac).
To search for language exchange partners, you'll need a version of Skype that provides "Skype Me" mode. Unfortunately, Skype 5 and beyond disabled this feature because there were too many perverts were using it to harass users who didn't understand what it was. As a result, you will need to download an older version (Skype 2.8 for the Mac, 4 or lower for the PC) to be able to search for users and be searched for. Thankfully, because Skype has so many users, there are still plenty of people to message even though "Skype Me" hasn't been available in a new version for a couple years.