With nude pantyhose, there's no fuss, no complicated color coordination; it's just all you. This bare look is good for certain styles of purple dresses -- namely, slinky styles that are more formal. If the look of bare skin is what you want, nearly bare will bring out the richness of your dress's design as well as the luscious look of your skin. Wear nude hose especially if you've got a pair of strappy shoes with heels.
Tan and brown pantyhose complement the color purple in a subtle pairing with a touch of earthiness. Try this color of hose with a dress that's a lighter shade of purple and a style that's more casual daywear than fancy and formal.
You can wear black pantyhose with a purple dress, but this look takes some special consideration. For starters, wear only opaque black hose, not sheer ones; the solid black is what sells the look, not a greyish sheen over flesh. This is also best with a shorter, sportier dress with a skirt no longer than mid-calf; the black hose need to be obvious and deliberate. Also, help sell this look by dressing up some other part of your outfit with black in the form of, say, a sash, a hat or some gloves.
Yellow is a great color to pair with purple because they're opposite on the color wheel. This makes for a pleasant contrast, but this striking look does have a decidedly casual quality to it. In other words, it's probably not a pairing you want with a formal, purple satin dress.
Purple pairs with purple if you can find hose that match the same shade as your dress. With this pairing, though, make sure to pepper yourself with some other colors somewhere else in your outfit so you don't get a case of the monochromatic blahs. A bit of black, yellow or silver in your shoes, purse, cardigan, hair, sash or other accessories will make this work.