Whenever you think you have found a bug in Blender, there are a few steps to ensure it is really a bug, and if so, that it is handled correctly. Following the steps set out below will make life easier for you, the user, and us, the developers.
Keep in mind that the bug tracker is not intended for feature or support requests.
We can only support the Blender binaries as have been distributed on blender.org. First thing to test is therefore always if official releases have the error. And if there's an error, test it with at least one older official release to verify. This can reveil problems with your graphics drivers for example, it's not likely that big errors are there for many releases!
If the error is in current svn, try a build from someone else (http://www.graphicall.org) and when possible test it on another system.
Before you think of posting any bug report, consult first the bug tracker for an existing report on the bug you have spotted. Make sure you search from all bug reports, also closed and deleted ones.
It may very well be that the bug has already been spotted.
First try to simplify the process that triggers the bug, so that it is reproducable in the least amount of steps, and with the simpest .blend file possible. The simpler the case, the easier it is for us to spot the problem in the code.
Very important is, that the bug is reproducable, that is, not occuring on a random basis.
A .blend file illustrating the bug is essential for the process. Carefully reducing complexity in files is also a great way to help developers to find issues.
Apart from the actual bug report it is always good (if not necessary) to include operating system, software (drivers) and hardware specifications of your configuration. Some bugs can be related to either area and including this information can help the developers pinpointing problems better. And let's not forget mentioning what Blender version you are using. If you are using a SVN build, please look in the splash for the build date (Help > About... ) and include that as well.
If you use Blender 2.5x, attach the system-info.txt that is created when selecting System Info from the help menu. You will find the text in Blender text editor with said name.
For example: