Clerks was shot in black and white for budgetary purposes, they just didn't have the money to film it in color.
Frances Ha was filmed digitally (Color) and in black and white, and was done in b&w to evoke reminisces of movies such as Woody Allen's Manhattan, or works by Truffaut.
I cannot find any references explaining why La Haine is in black and white, but considering that it was filmed during riots and contained other raw footage type scenes, it may have been both a budgetary and dramatic effect choice.
Originally, color film was available as early as the 1920's, however it was very expensive to work with, and as the development process was not very robust, colors could change depending on chemicals used and time exposed. Additionally, there were not very many cameras available that could utilize color film.
Technicolor developed a fairly consistent, robust development process in the 40's, and in the late stages of the decade was forced via anti-trust to license their process royalty free. This made color filming much more available and cost effective, and color slowly became cheaper than black and white.
Black and white is now more of an artistic choice. As stated by Roger Deakins (Principal photographer on The Man Who Wasn't There) in this article:
[Black-and-white] focuses you on the content and the story, and it really concentrates your attention on what's in the frame. All too often, color can be a distraction -- it's easier to make color look good, but harder to make color service the story. Black-and-white imagery is much more about the balance between the light and shade in the frame, and I think it can help convey story points a lot better with fewer distractions.
Lighting is not only about lighting; it's also about not lighting, and cutting light off of objects as much as shining light on them. Those kinds of considerations are as important in colour photography as they are in black-and-white, but the sheer beauty of a well-composed and well-lit black-and-white frame is hard to beat, because it's difficult to produce that type of focus and simplicity when you're shooting in color. It's vitally important to be able to separate shapes and surfaces through the use of light and shade, and to focus the audience's attention on what you want them to see. Color is seductive, but it's harder to get past the surface gloss to create a truly simple and relevant image. I almost wish every film were in black-and-white
Note: The above referenced article has quite a few links regarding use of black and white, including references to using it to distinguish between two worlds in a movie, (Such as Wizard of Oz, Purple Rose of Cairo), and statements by directors essentially that it evokes an other worldliness and/or nostalgia and memory.
With digital cameras and editing, the process can become easier and much less expensive, as there are programs and tools available to take a color image and convert to grayscale. There are two main methods, luminosity (assigns a shade of gray based on brightness of tone), and color altering which alters the colors themselves before the conversion. (There are only 256 shades of gray available, while modern color has over 16 million shades).
Modern cameras also have settings to mimic various types of black and white film, such as Afgapan (Afga was/is a German company that developed color methods around the same time as Eastman Kodak/Technicolor), Ilford and Kodak.