You probably are getting Google search suggestions in the 3 search bars (on the navigation toolbar, built-in home page, and built-in new tab page). If not, you can turn on search suggestions using one of these 3 methods:

• right-click the Search Bar (the one on the main navigation toolbar) > Show Suggestions
• click the magnifying glass icon on the Search Bar > Change Search Settings, then check the box for Provide search suggestions
• click the magnifying glass icon for the search box on the built-in home page or new tab page > Manage Search Engines, then check the box for Provide search suggestions

Those do not appear in the address bar yet. For now, you might want to check out this extension:

https://addons.mozilla.org/firefox/addon/omnibar/

I need that suggestions on URL BAR (address bar) and not on the any other bars. Now I see that only third party extensions can give me what I need (address bar with search suggestions)... I am very disappointed because other browser have only one bar for everything as you know. I do not want to use any extensions because that is a basic functionality and I will not feel secure to use third party extensions on my address bar.

Now I go back to the Chrome Browser as my default... and I will back when FF will have one bar for everything... and no so useless other bars.

It's an address bar. Google Chrome has an omnibar..

If the omnibar addon adds the functionality you are looking for, why are you so quick to leave without trying?

I know that it is an address bar in the FF and what is in Google Chrome and other browsers. I tested that extension in FF (and other similar extensions)... and everything works OK. But, as I said, it should be a standard functionality form "the box" and not achieved by the extensions.

Actually it is called Location Bar in Fx as Address Bar is more IE.