I especially love 'A Case of Immunity'. The confession by Hassan Salah is one of my favorite scenes. The wonderful give and take between Columbo and Salah (played so well by Hector Elizondo), the surprise appearance by the King (another solid performance - by Barry Robins) and the use of close ups and angles by Ted Post all make for a memorable gotcha.
Hassan may not be one of the sympathetic murderers, but he's such a "gracious winner" (when he THINKS he's won) that I hate seeing him get caught for that reason.