Yes, I think people often do become instinctively aware of being watched. It's probably through some form of telepathy, I would think...or kind of like radar picking up a blip...or a radio picking up an unidentified signal coming in.

Animals are, I think, far more aware of it than people. They almost always become concerned at some point that they are under observation, although they don't yet know by whom or from where. They get nervous and begin looking all around. I've seen this many times while watching animals and focusing strongly on them. I think this is mainly because their heads are not as full of idle and distracting thoughts as people's heads are. Your own inner "noise" or mental static can block the awareness of an incoming signal, and it often does so with people.