There are as many innovative, magical and contemporary settings out there as there are traditional, ageless classics for diamonds. Indeed, if you cannot find a setting that you like but have an idea in your head, you can simply find a jewelry artist or design group and collaborate on the design yourself, though with the enormous amount of available settings this often seems hardly necessary.
Most obviously, you should choose your setting first and foremost depending on the personal taste of whoever is to wear it. If you are buying the diamond for yourself, the best thing to do is to thumb through a few jewelry magazines, looking at the advertisements to find what you most like. If you and your partner are in on this purchase and selection together then the two of you can consult.
First, here are a few tips on which styles complement which fingers and hand types. Keep in mind this is entirely subjective, and just an amalgamation of opinions.
Sometimes even oneself is not the best judge of what looks good on one's fingers. In general if you have long, bony fingers, and/or muscular hands, a larger, thicker ring with a more prominent stone or stones flatters your hand. If you have large hands and long fingers, you are probably the only type of person who can look good in a large pronged setting, in which the diamond sticks out from the ring. You are terribly lucky, because these kinds of rings are often the simplest style and really do show off the stone over and above the setting. You are also unlucky should you get stuck with a ring like this and not be able to wear it because it does not fit your lifestyle. For instance, if you do a lot of work with your hands, a pronged setting can be a setback-- the stone will snag on your clothes and scratch your desk. Whether the setting is classic 20th century (think something a President's wife or the late great Princess Di might wear-- modern but not postmodern!), minimalist modern, or antique is up to your own sense of taste, so long as the setting is thick and the ring large.
If you have rather wide and short fingers, a medium sized ring with a large stone can look gorgeous, so long as it remains flat against your hand (try to stay away from pronged settings, in which the diamond seems to jump out from the ring). Again, the style is up to you-- what goes with your casual and evening clothes.
If you have small fingers that are thin and delicate, thin and delicate settings complement your hands quite nicely. And those with short fingers should stick to small stones. Again, the choice of style-- antique reproduction ("repro"), modern, or classic-- is up to you, but you should try to keep it simple so that the ring does not swallow your hand. For example, classic 20th century (President's wife) styles would not look good on small hands, because such styles tend to swallow up the finger.