Everyone knows that the Eyedropper Tool picks up or samples color, but did you also know it will apply color?
With the Eyedropper Tool selected, hold OPT/ALT, and click on a path or object to instantly apply the active color–either fill or stroke, depending on which swatch is in front at the bottom of the Tools palette. You needn’t even select the object before hand!
Using this method, you can recolor an entire drawing more quickly than the usual route of selecting an object, clicking a swatch on the Swatches palette, and moving on to the next object.