The default action for searching with the Firefox toolbar is to open the search in the current tab. This drives me crazy, but thankfully it’s easy to fix.
New Search Tab with Hotkey
Just search using Alt+Enter instead of hitting the normal Enter key. This will work even if the default is still the current tab.
New Search Tab by Default
Type about:config into the address bar, and then put the following into the filter box:
Double-click the value to change it to true.
New Search Tab with Tab Mix Plus Installed
Open Tab Mix Plus Options through the Tools menu. Click on Events.
Check the box for “Search bar” under the “Open tabs from” section.
New Search Tab with Middle-Click
You can also middle click the search button after entering text into the search box. (Thanks to markdr in the Lifehacker comments for this one)