Will Intel still be processor king in 2020? Perhaps. Perhaps not. But, they certainly intend to be around then, and still making processors smaller, faster and less power-consuming.
In fact, Intel plans to abandon some of its future research projects in order to make certain that its processors improve in this way, and are subsequently looking into technologies such as carbon nanotubes and nanowires to shrink transistors down as far as they can - even down to smaller than the atomic level. The current 90 nanometer process technology should be long out of date by 2011, when Intel plans to have mastered a 10 nanometer process technology! And by 2013, processors will be made of entirely new materials!
And beyond 2013? Well, Intel has its eye on Spintronics as the new technology of the 2020s. Spintronics is the study of spinning electrons, and the magnetic fields that are produced when electrical charges revolve. This technology could be used to represent the "on" or "off" state of a transistor. More here.