Giuliani broke much of the Mafia control in NY. He also aggressively policed NYC with the Borken Windows theory, Stop and Frisk (as mentioned), and Compstat. Most working people loved him at the time, it's only now that they've had 20 years or so of benefit from his policies that they bitch about him.
Also a lot of criticism is leveled his way from some because he made NYC a bit dead city in term of nightlife and the arts. He continued Koch's vision of cleaning up Times Square, regulated the clubs, bars, etc.... more vigorously, etc.....