TAB and SHIFT + TAB
This one seems to go without saying, but instead of manually clicking between various text fields while typing, just hit tab to jump to the next consecutive one. And this applies throughout OS X and to any sort of fields. For instance in Safari, press TAB to jump from the URL field to the Google search box, and press it again to jump to the Top Sites section and then to the History search field.
What is less obvious, however, is that pressing SHIFT + TAB is the equivalent of a reverse TAB.
Thank you to "joec" from the comments on this post for pointing out these shortcuts.