While concurring with Bomber's praise for NATS controllers in the UK, I am still awestruck by the volume of traffic that New York Center keep apart during approaches to JFK/ La G/ Newark and Teterboro. Even with the TCAS on 6 mile scale, I still can't see a gap to fit through!
That said, I have had 3 RAs going in to TEB, all caused by the minimal separations that the SIDs/STARs require......often only 500 ft as mentioned by phil94028 in his post.
NATS and Eurocontrol have made several pleas to operators to ensure that they only approach their cleared alts/FLs at less than 1,000 fpm, in order to reduce nuisance RAs, but unfortunately the message is either being ignored or not sufficiently well promulgated to the rest of the world's aviators.