Technically, film noir is historical description - i.e., American crime dramas made between 1940 and 1958. I say “1958” because the end of noir is generally considered to be Orson Welles “Touch Of Evil”, the ne plus ultra of noir. (If you haven’t seen it, do so. For my money, it’s a better movie than Citizen Kane.)
Any film after this period is “neo-noir” - there seem to be periodic outbursts of Hollywood neo-noir every fifteen years or so as new generation discover the classics. The neo-noir period of the 1970s was particularly fertile in that it created a handful of movies (Chinatown and The Long Goodbye, especially) that could stand up to the classics.
Besides the ones that have already been mentioned, Robert Aldrich’s Kiss Me Deadly should be required viewing. For one thing, you’ll understand Pulp Fiction slightly better. For another, it’s one part crazy style (dig the reverse credits at the end) to one part brutal violence. Aldrich inverts the usual noir formula by portraying Mike Hammer as a meat-headed thug who basically punches his way to the finale. Awesome, awesome movie.
Gun Crazy was already mentioned, but it has one of the best scenes in noir - a real-time handheld camera shot of a bank heist. The rest of the movie isn’t as good, but that scene kicks ass.
Another personal favourite: Detour. Made by B-movie king Edward Ulmer, Detour is a key film in the cycle mostly for it’s deeply strange narrative. Saying anything more is ruining it, so watch it for yourself.
Also, no examination of noir is complete without a quick viewing of some Fritz Lang classics. German expressionism was the main wellspring for noir’s visuals, and nobody did expressionism like Lang. The well-known ones (especially M) are all worth watching, but see if you can track down a lesser-known one called Hangmen Also Die!, which has some outstanding black & white cinematography grafted onto a heavily political storyline.