Warwick is a champion particularly well-suited for killing monsters in the forest. Hungering Strike can sustain your health, especially if you are able to get the Ancient Golem's blue buff.
Warwick's ultimate can stack on-hit effects such as the Black Cleaver or Wit's End.
Warwick is a very strong jungler. Clairvoyance can help you keep track of his position and enable ganks.
Warwick is a very strong 1v1 champion, especially late in the game, so stick with your teammates to make him less effective.
Warwick can solo the dragon on Summoner's Rift early, so try to prevent him from killing it throughout the game.