Tip: Walls of Text
Please, avoid copy/pasting the content of text files like system-info, debug/console/command line output, scripts directly in the report's Description field. It makes the report difficult to read and breaks up the formatting. Include them as files instead (.txt). On how to include files, look at the Appending files to the report section.
Bugs in Blender or Addons included with Blender can be reported at developer.blender.org, through links on the front page. You will need an account, so that developers can follow up with questions and notify you when the bug is fixed. You will receive an email each time there is an update to the bug report.
The bug report page has concise instructions and a template for creating reports. More advice on how to create good reports is listed below. Following these steps will make life easier for you, the user, and us, the developers.
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 reproducible in the least amount of steps. The less steps there are, the easier it is for us to spot the problem in the code. Typically if you have a complex .blend file, it is possible to keep removing objects, modifiers, nodes, and other data until the problem has been isolated to a simple setup.
Very important is, that the bug is reproducible, that is, not occurring on a random basis. It is fine if the bug randomly happens for example 1 out of 10 times you perform some operation. However if the bug randomly happens without any clear steps leading up to it, then it is unlikely developers will be able to fix the bug.
A .blend or screenshot illustrating the bug will help to speed up the process. As in the previous paragraph, make them as simple as possible, so that the developers can spot the problem without too much effort.
You can even provide a backtrace which lead to possible crash. That may help developers as well. A backtrace is not necessary and producing a useful one requires special debug build and a debugger.
Tip: Appending files to the report
Files like .blend, .txt, images can be included into the report by dragging and dropping them into the Description field. At the bottom of the bug report page, there is a Preview of how the report will look like when posted. If everything is OK, a link will show up with the file name. In the Description field itself, the file is represented by a set of letters and numbers in brackets. To move the link to an appropriate place if needed, cut and paste it and be sure that there are spaces between it and the rest of the text.
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 to pinpoint problems better. And let's not forget mentioning what Blender version you are using. Please look in the splash top right corner for all build details and include that as well.
Tip: System Information
system-info.txt generated from the Help > Save System Info Menu will give information about the OS, hardware, drivers, Blender version and add-ons enabled.