It is sometimes used in place of watercolors because it dries closer to the color (slightly darker usually) while watercolor dries lighter, and often unpredicably to beginners. It also lays on smoother, leaving less brush strokes than watercolor once dry. It does however, differ from watercolor in that once dry it is no longer soluble.
It is used as an alternative to oil paint because it dries faster. Oil paint, using oil of course as its medium, takes a very long time to dry. Acrylic can achieve an oil-like effect in much less time. As an oil substitute it is limited due to the superior color range of oil, and the fact that acrylic creates a much more shiny, smooth, some would say "cartoonish" effect, not surprising since it is plastic.
Acrylic is also used for its ability to bond to many diverse surfaces.