In years past, fashion magazines have encouraged the average woman to punch up her everyday look with tights in a rainbow of colors - but the average woman is smart enough to know that fushia legs look ridiculous. However, a matte pair of tights can be very wearable and is a nod to current style.
Just to be clear, tights differ from pantyhose in weight - they are made of more dense material that provides full, saturated coverage, color-wise. Black tights and black shoes look great with a lighter colored dress, especially one that is flowy and ethereal. The black tights/shoe combo ground a dress like this and create a long line for your legs. Or pair them under a black skirt/top combo for a lean, monochromatic look. Accent with a brightly colored bag or strands of gold jewelery for maximum impact. For the truly daring, wear brightly colored heels (like white or yellow) with your head to (almost toe) black look.
Black is definitely the most wearable color of tights, but if you have a brown or mauve or gray outfit that matches your tights exactly (again, going for the monochromatic look) I say give it a try. If you absolutely must wear brightly colored tights, I like the slightly cheeky effect of just a flash of bright red tights under a knee-length skirt and black knee boots. If you really, really want to wear a pattern, make sure it's subtle (like the photo above).