This is the one of those rare films that has stayed in my "Top 10" since the first time I saw it back when it was only available on VHS in 1998. There are currently two versions on the market, with a theatrical R-rated cut being the most common. The version of the film I recommend is director Abel Ferrera's original vision, the infamous NC-17 version that includes all the Harvey Keitel nudity you didn't want to see but are forced to see anyway (and it's hilarious in its disturbing context within the movie).
Harvey Keitel is a corrupt cop of the highest extent, taking his power as a New York police detective and using it to cover his drug and gambling addictions. The film explores all of the dirty holes (no pun intended) that a person of such low caliber can fall into, but takes it to places that still to this day make me cringe in unpleasantness. The lengths at which Keitel's character goes to satisfy his own sick desires in the world of drugs and sex are both disturbing and somewhat comical in that "I'm not sure if I should be laughing at this, but i will only because I could never see a normal person doing this kind of shit" way.
Harvey Keitel kills it as the Lieutenant (on imdb.com his character name is simply listed as that; much like Edward Norton's character in "Fight Club", no actual name is ever muttered), a man who has to confront his sinful ways in the wake of a case involving a brutal murdering of a nun. Along the way the man becomes embroiled in his addictions, as well as having some of the worst luck involving baseball gambling a man could ever have.
One of my favorite scenes is later in the film, with the Lieutenant sitting in his car listening to a Dodgers/Mets game. Having bet against his hometown team in the beginning of the film (and losing thousands of dollars in the process), he bets for the Mets just when Daryl Strawberry decides to hit a game-winning home run. Keitel pulls out his revolver and blasts his radio while screaming loudly in racial slurs...all with his window down and in traffic. People stare at him, and in defiance he quickly puts his sirens on and speeds away. Seriously one of the funniest film moments I can remember outside of a traditional comedy, and in a circumstance that is neither funny nor rewarding in any kind of comical sense. It's just funny because it's an easily-relatable incident that all people could fall in should they give in to their overwhelming desires without thinking about the consequences.
What we get in the end is a redemption film of a man who has to confront his inner demons (so many of which we are uncomfortably forced to watch, including one of the most vile traffic stops you could imagine involving two teenage girls), including a whole lot of crying from Harvey Keitel. If an award were to be given out for the "greatest crying in motion picture history," Keitel would get the Lifetime Achievement Award for this film alone. He's probably the only man who, if someone presented you with a sound clip of a man crying, his would be the only one easily and immediately recognizable.
For me, what makes the film so great is not the unintentional (or intentional) discomforting hilarity (which is only apparent because of our rampant discomfort from the dastardly deeds he involves himself in - much to the genius of Abel Ferrera's direction), but in the moments leading to the Lieutenant's visions that force him to confront his evil deeds.
A follow-up film was made that is in no way related to this version (other than by title and total character craziness) called "Bad Lieutenant: Port of Call - New Orleans" and starring Nicolas Cage in a role that was cater-made for him. That film is more cerebral and off-the-wall from director Werner Herzog, but is nowhere near the caliber of film that Keitel's original was. 1992's "Bad Lieutenant" has purpose amongst the dirty character-study roller coaster it takes us on. 2009's "Port of Call" is more about exploring the drug-induced craziness of Nicolas Cage that may or may not have been "acting".