This page will tell you your Kindle's default root password. It can be calculated using your Kindle's serial number.
There is another (unprivileged) login on most Kindles: User framework with password mario.
There are different reports with different Kindles and different firmware versions. I have verified the result on a Kindle 4 with 4.0.1 firmware and heard positive reports for firmware 5.1, but it should also work on other Kindles and with other firmware versions. Just try the four possible passwords. Good luck!