From a few posts and comments I’ve read in the last couple of days, it seems to me there is a hidden behavior and preference in Firefox that is not very well know: By default, if you press Alt while pressing Enter in the search bar, you will get the search results in a new tab. The same goes for the location bar.
If you find yourself always doing this, you can make it the default behavior by setting browser.search.openintab to true in the advanced preferences (enter about:config in the location bar).
Now behavior is reversed: when you press Enter in the search bar it will automatically open the results in a new tab. If you want to open them in the current tab, then press Alt + Enter.
In case you wonder, I believe this behavior is as old (and undiscoverable) as Firefox.
Edit: Yochanan points out in the comments that you can also middle-click on the search button to automatically open search results in a new tab. It also works with the go button in the location bar. Thanks!