We always give a five finger wave to all police/policecars, never know if you ever will need 'em on your side.
Have had numerous good experiences with help from police, inluding a lift home when we cracked a rim on our tandem.
Also had a squad car go on the bullhorn telling us we we're doing 30-some odd miles per hour on a good downhill.
Hey, they've got a job to do and the majority do it quite well!