Firefox and Opera, by default, have a search field (it's a text field but Firefox calls it the search bar) to the right of the address bar. I've removed mine--it's redundant and cumbersome (or so I thought, but see point 3 below), and an information leak.
I often have students in my office for advising and typically go over their online records. This means they look at my web browser. This also means they can read titles of tabs (fine, so be it) and contents of the search bar. I'd hate to have a student read too much into the fact that I've recently searched for Shaun Cassidy. So in my office I removed the search bar and just open a new tab (^t) and hit the g key. This takes me immediately to Google.
(1) Most of my searches are Google searches. I played with Bing when it first came out, but Bing's results don't seems as good, and Bing seems to use a fair amount of client-side scripting, which I'd rather avoid. Google does too, but they already know everything about me.
(2) I may sometimes prefer a Wikipedia search or some such, but very often the appropriate Wikipedia page is near the top of the search results, so Wikipedia search is redundant.
(3) Doing a quick lookup for this posting led me to http://www.mozilla.com/en-US/firefox/search.html, which points out that one can select text and drag it to the search bar, which seems to work well. So my search bar is, at least temporarily, back in my Firefox window on most of my machines--just not the one in my office.