Currently, the most advanced commercial processors use transistors with a gate width of 45nm. 32nm processors are coming soon. 22nm technology exists, and SRAM cells have been created in this technology for research purposes.
According to the International Technology Roadmap for Semiconductors, a report produced by the major players in the industry, the CMOS technology nodes will reach mainstream status at the following times:
However, it is unclear whether 16nm and below will be technologically possible. For reference, a silicon atom is about 0.3nm across, so the gate would be less than 40 atoms long in an 11nm device. Clearly there is a fundamental limit that will be reached shortly.
As to what might replace CMOS transistor technology, it’s hard to say at this point. Carbon nanotube technology is showing promise, but it’s still very much in the research stage. I don’t know of any other suitable candidates at this time.
Also, there is an alternative to building faster processors - running more processors in parallel. Already most commercial processors have multiple cores. This is one way to stave off a performance plateau when the limit is reached.