There is often discussion about efficiency of different trading systems. Is there some stock exchange using open outcry trading as of today?
As Chris pointed out in his comment, smaller stock exchanges may use open outcry. There are several exchanges that use open outcry/floor trading in the US, however, although they aren't necessarily stock exchanges.
Having visited the three Chicago exchanges I mentioned, I can personally vouch for their continued use of a trading floor, although its use is declining in all three.