There are different ways to prevent this. Pls look at the screen shot for reference.

     * If you dont want firefox to remember any passwords uncheck the option that says remember password for sites.
      *In case you want it to work only for specific websites add an exception.
      *U can also delete the paswords that has been saved already by clicking on saved passwords and remove the saved passwords.

Note: Do remember that some websites like msn messenger etc remember the passwords if u just close the window.so try to log out the webpage before closing it.

                                              Regards,  
                                                              Kiran

Is your problem about filling the name and password automatically or about a website remembering you and log you in automatically?
The latter is done via a special "remember me" cookie.

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of your add-ons is causing your problem (switch to the DEFAULT theme: Tools > Add-ons > Themes).
See Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems and Troubleshoot issues with plugins like Flash or Java to fix common Firefox problems

The recommended solution steps did not bring me to the location that the solution recommended.