Is there keyboard shortcut to move input focus to the Google Search box?

Update: This does not seem to be working anymore. Press ESC to move the cursor back into Google's search box.

If you search for something in Google Search …

… just begin typing again. For example, writing "unicorns", then " magic" (that is, space, then the next keyword) will automatically focus the search box again.

Note that you need to enable instant search from your settings:

Finally, you can also press ⇥ (Tab) to get a manual selection for the results – navigate through them with ↓ or ↑, and open them with ↩.

Ctrl+K in Chrome not only moves your courser to the Google ommibox, but it also clears it, saving you the extra keystroke.

F6 is another way to get to omnibox, and will always work, whereas key combinations may also depend on where your mouse courser or focus is; for example, on SE, Ctrl+K is the shortcut to add code to a question or answer.

In Google Chrome, you can press Ctrl+L to focus the address bar. This would allow you to perform a new search instantly.

In case you want to focus the search box on the actual Google website, please refer to slhck's answer.

You can also enable Instant inside Google Chrome by checking the following setting: