Minecraft wiki entry for Dropper, associated text: A dropper can be activated by:
an adjacent active power component (Exceptions: a redstone torch does not turn ON a dropper it is attached to)
an adjacent powered opaque block (strongly-powered or weakly-powered)
a powered redstone repeater or redstone comparator facing the dropper
powered redstone dust configured to point at the dropper, or on top of it, or a directionless "dot" next to it; a dropper is not activated by adjacent powered redstone dust that is configured to point in another direction.