John's answer traces the multimedia history of the Patlabor franchise, starting with the 1998 manga by Masami Yuuki, and examines the fundamental traits that have made Patlabor so popular. He even points out Patlabor's influence in recent series, including a current favorite of mine - Toshokan Sensou/Library Wars.
Tonally, the influence of Patlabor also seems evident in the Toshokan Senso franchise, which got an anime feature film last June. In appearance and personality, Toshokan Senso’s protagonist Iku Kasahara could almost be a sister to Patlabor’s protagonist Noa Izumi. In terms of series construction, very reminiscent of Patlabor, Toshokan Senso revolves around a small, quirky team of law officers who spend most of their time on mundane activities and interactions, only occasionally launching into militaristic action.
Overall, if you have been waiting for a signal - any signal - that people are still interested in watching a series about police Labors and the loveable goofballs that pilot them, AnimeNation has you covered. Personally, I would just love a re-release of the Mobile Police Patlabor 1989 series with an affordable DVD package; currently, they all cost an arm and a leg for 15+ DVDs each only holding about 4-6 episodes!
Also, I could definitely see a live action Patlabor going down if the studio doing it could make the necessary CGI look good as well as keep the original camaraderie of the Second Special Vehicles Division as it is in the series.