Formula One drivers in the early 90s were the only ones really able to come close, with shift times between 150 and 200ms. The average person is more around 300 - 400ms when shifting aggressively. You can be faster than 300 - 400ms, but not with 100% consistency, especially on downshifts, and especially with some transmissions with odd clutch engagement points or shift levers that require more deliberate effort.
A modern DCT, like Porsche's 2nd generation PDK, has a shift time of 150ms. Porsche's 3rd generations are even faster -- the PDK-S in the new GT3 is 100ms. The version in the 918 Spyder is 50ms. All of these are perfectly rev-matched, every time.
I've driven many tremendously good manual transmissions. However, generation two PDK is good enough that after four test drives (two with a 6-speed, two with PDK + Sport Chrono) I've actually decided to order my Cayman S with PDK since it's unquestionably better. The only thing I wish is it had the "burnout/donut mode" of the 3rd gen.