This has been really bugging me for a while too and I just found a solution so I thought I would share it.

Go to your firefox profile and the 'chrome' subfolder. Open the userChrome-example.css in a text editor and paste the following text at the bottom:

#addon-bar
{
  display: none !important;
}

Save the file as userChrome.css in the same folder. Restart firefox and no more addon-bar :)

If you still want to see addon information that is displayed on the right side of the addon-bar you can use the 'TotalToolbar' addon (from http://totaltoolbar.mozdev.org/) to move that block to another toolbar. I put mine on the right side of the navigation toolbar.

Thanks hatcher29... Problem solved.

For newbies.... here is the solution explained in detail

Create a file userChrome.css in the chrome subfolder of the profile folder of firefox. For this click on Start -> run > Type in %appdata% and hit OK. This will open application data folder or appdata\roaming if you're in vista. From here browse to Mozilla \ Firefox \ Profiles \ xxxxxxxx.default (this is your profile folder). In here you'll find the folder Chrome Enter the folder chrome and create the file userChrome.css

In the file enter the code mentioned by hatcher29

I tried to do this step by step and it didnt work maybe i did something wrong can u upload pictures so i can see how it is done?

update:

I did it! It took awhile but i finally got it.

i never could find the chrome subfolder

For me, the chrome subfolder was located underneath 'extension' after i clicked the xxxxx.default. Then, I had another xxxxxxx folder and it was located underneath there. Hope this helps :/