Firefox only: (Win/Mac/Linux): Firefox extension KwiClick opens a dedicated search dialog that finds results from Google, YouTube, Wikipedia, Twitter and more without having to leave the page. It's a search box on steroids.
Once you've installed the extension, you can access KwiClick from the new button on the toolbar, which will open up the dedicated search dialog. You can drag this window around your screen anywhere you want, choose the providers you want to search with, and load the results directly in your browser window without having to close the dialog. The search box has autocomplete, the next and previous buttons page through results, and you can easily pick the search providers you'd like to use.
Where the extension really shines is searching YouTube, Wikipedia, or Twitter—just type in your search terms and pick from the results, and you can watch a video directly in the standalone window, read the Wikipedia article, or access a twitter stream just by typing in a keyword. If you didn't use it for anything else, it would make an excellent dedicated YouTube widget that you can put wherever you want on your screen. KwiClick is a free download, works wherever Firefox does.