In Firefox, one of the awesome bar's awesome tricks is guessing which URL you meant to type. It does it by querying Google and using the Browse By Name search feature to take you directly to a site.
For instance, if I just type "http", Firefox can't find anything definitive in the history for just that part of a URL, so it kicks it over to the keyword search. Google takes you to the top search result for that keyword, which is the Wikipedia article on HyperText Transport Protocol.
But, if you don't like Google, you can change that.:
Type about:config in the location bar and press return.
This takes you to a warning, asking you to be careful. Do be careful. Once you're sure you mean it, press the "I'll be careful, I promise button."
Now type keyword.URL into the box marked Filter.
Double-click on keyword.URL and a dialog box will pop up with a Google URL in it. This is the URL the awesome bar uses to do a search when it can't make sense of what you typed.
I suggest saving that URL somewhere, in case you want it back. Though it is currently in the article for keyword.URL at MozillaZine.org.
In the text box, replace the URL with whatever search engine you'd rather use.
Now go to the awesome bar and for a test type "http" again.
Instead of taking you to the Wikipedia article, it gives you Bing search results for http.
You can change the keyword search to hit other sites, as well.
For instance, Scroogle is a site that returns Google results without your IP address being logged or cookies being set.
And Nathan Thompson, Class of 2011, e-mailed me about how he's using CNET search to power his keyword lookup in Firefox. He just uses the cnet.com search string and ends it after query=.
That, my friends, will give you a few more options to tweak your Firefox awesome bar's awesomeness.