You can do this with Firefox currently. You can remove the search box from the UI using "View > Toolbars > Customize..."

Any term you type into the URL bar that Firefox doesn't recognize as a URL will default to a google search. I actually edited this in about:config to default to a secure google search rather than a basic google search.

If you want to get more advanced, you can set keywords to perform custom searches. I have mine set so that typing "w <string>" will search for the Wikipedia article. I use several others "i <string>" for image search, "n <string>" for news, "d <string>" for definitions, and so on. They're easy to set up.