To dream that you are staring at something or someone indicates that you need to take a much closer look at some situation or relationship. Perhaps you need to approach a situation from another perspective or viewpoint. Alternatively, staring represents your passivity. It is time to start taking action.
To dream that someone is staring at you suggests that you are hoping someone would look your way more often. It may also represent anxiety or pride. Alternatively, the dream suggests that you feel overly scrutinized for your actions and behavior.