Most of the fastest knitters in the world favor a style of knitting that's sometimes known as lever knitting, pivot knitting or Irish Cottage knitting. It's a great method for knitters who knit for a living to use because it allows you to knit really quickly and doesn't cause as much pain in the hands and joints as other methods.
Lever knitting is a sort of variation of English knitting in that the yarn is held in the right hand. But it's different because one needle is held stationary while the other does all the work.
The yarn is usually tensioned around the lower fingers of the hand and the hand moves back and forth to form the stitches. It's a fluid movement that cuts down on repetitive strain and is historically used by production knitters who need to be able to work for many hours each day without pain.
Perhaps the most famous proponent of lever knitting is Stephanie Pearl-McPhee, also known as the Yarn Harlot, who teaches classes on the method, which she learned from her grandmother. (Here's more on one of her speed and efficiency classes; I've taken a shorter version but haven't practiced the method much.) The world's fastest knitters also use this method.
It's easily learned on long straight needles, one of which you can pop under your right arm as you work, keeping it stable. That way only the left-hand needle moves. Once you're comfortable with working that way, you can also perform the same actions with circular needles. A knitting sheath or makkin can also be used to hold a straight needle stationary (and that's what you'd probably use if you were knitting while standing or walking).
Heartstring Fiber Arts has a nice explanation of the style on its blog as well as still and animated photos to walk you through the process.
Blogger Maven Knits (check her site for a couple of videos) credits learning pivot knitting with eliminating the pain she felt in her hands while knitting in other styles.