A friend brought up the topic, so I thought I'd jot down a few ideas here. These thoughts are very much under construction so I might update this in the future.
1. Old-shtyle ishtyle: The least charitable reason, but not entirely devoid of substance. "Old" is a pretty good excuse to say "classic". And a sense of history, a hearkening back to the good old days is always a nice feeling. For instance, how about this swingin' 70's concert pic? Ah, what a time it was, it was!
Actually, the picture was taken in 2004. The guy's called Eddie Roberts and he was performing with his band The New Mastersounds in Chicago. BW insidiously warps our minds again.
But now on to more intrinsic things:
2. Emphasis: Sometimes, the dominant forms and patterns in a scene are most strongly defined by shades (lightness or darkness) and not by colours. Most significantly, the three-dimensional structure of objects is conveyed entirely through shading -- if you've ever cross-hatched a pencil drawing of a vase or a face you'll know what I mean. Bright colours distract our eyes from these patterns -- a bright yellow flag in the background can ruin a sober portrait, and colourful designs can obscure the roundness of a vessel or the clean lines of architecture. BW emphasizes just the shadows, highlights and contours, which is where the communicative forms of a photograph frequently (I would stick my neck out and say "usually") lie, and strips away the chromatic junk.
3. Clarity: With just two colours (or strictly speaking, just one colour -- grey) our visual language is immediately restricted. So the messages we manage to convey through our images are likely to be simpler and more direct. Result: a much greater chance of effective and unambiguous communication.
For an example of 2 and 3, here's Ansel Adams' "Aspens". There are three visual elements -- tree in foreground, treetrunks in background, and dark forest beyond. There are three dominant intensities -- bright white for the tree, medium white for the trunks, and dark grey for the forest. And that's it. End of story. The sparsest possible language is chosen to perfectly separate all three elements and the impact of the resulting image says a lot for economy of expression. Colour would be unnecessarily verbose.
4. Coordination: A camera allows you plenty of control over exposure, i.e. over the darkness and lightness of objects. What it can't do is give you any sort of control over colours in your image -- filters or exotic films limit your options to colour casts or weird fixed palettes, and extensive digital post-processing is... umm... not really photography, is it? So that brilliant bazaar shot you thought you nailed the other day turns out to be a dud because Mrs Ray and Mrs Ghosh, the chief protagonists, wore hideous pink and blue saris respectively. Shooting BW keeps your colours (dammit, you have just one!) nicely matched. In fact, many excellent colour photographs use small, well-coordinated palettes.
Here's something that works in BW but would definitely NOT work in colour if the clothing and the umbrella were of different hues (which is quite likely). Note that the colours wouldn't necessarily clash, but the picture would still lose unity in the foreground.
4a. Shadows: Cutting out colours introduces interesting resonances between objects and their shadows. These pictures say it all:
5. Rawness and Simplicity: A much-heralded quality of BW is its capacity to render stark and gritty images. This is probably why so many urban photographers use BW -- the clamour and grime of a big city is an ideal BW subject. The favourite film of these street shooters used to be Kodak Tri-X, well known for yielding somewhat grainy images. This feature contributed to the slightly raw and rough-edged look we've come to associate with classic street photographs.
Let me reiterate this: BW is essentially simpler than colour. We associate simplicity with the past, with rural life, with congenital traits, with our primitive instincts to be happy or sad or combative, and so on. And BW excels in capturing these aspects of our world.
6. Abstraction: Verisimilitude is never the principal purpose of art. This is a nuisance for photography, which is burdened from the start by the fact that it mimics reality by default. So over the years, photographers have looked for ways to express themselves through their pictures, to make us look at the world through their eyes. BW immediately distinguishes between the real and the virtual by discarding colour, and thus in a way establishes the communicative credentials of the image -- it sticks out and hence seems more meaningful.
Of course, at this point we must admit that BW was not devised because of its potential for abstraction -- it was a consequence of the limitations of the technology of the time. And when colour film was invented, BW's exit seemed preordained. But that didn't happen, and even today many many people who shoot to tell stories stick to BW.
- Biplab makes a case for small palettes and strong separation of elements in "Why I both like and dislike Ansel Adams...". Clarity of expression does show clarity of thought, and the argument is convincing.