TCAS II is a fantastic tool. However, when pilots fail to follow the RA (Resolution Advisories) Climbs and Decents serious problems can arise. Eurocontrol has put out newsletters talking about several incidents, with both correct and incorrect pilot responses. There have been several near misses and the proximity is very scary.
The biggest threat is when ATC gives instructions for one aircraft which contradicts TCAS II directions and the pilot does what ATC says. The worst example would be the mid-air over Switzerland with a DHL airplane and a Russian airliner in which (correct me if I am wrong) the Russian airliner followed the directions from the Swiss controller which was oppisote to what the TCAS told them to do.
I have had two RA's in the past four years, both climb commands. One was due to VFR traffic while on vectors to the ILS into Stuttgart, GE. The controllers were very disturbed by the event and appologized to us. The second event involved an Airbus climbing to level 1000 feet below us over Austria. He was coming up so quickly, however, that we got the climb command and shot up to the next Flight Level. Wien radar was upset that we climbed and scolded us for doing so, but he didn't know if the Airbus crew had mis-set their altitude pre-select, or if the AP would fail, or if the crew was hand flying and distracted, or if they had mis-set their altimeter.
Lesson here: Do what the TCAS says to do regardless of what ATC says.