You might joke about your neighborhood stalker who always seems to know where you've been and what time you get home from work every day, but it can actually be a little creepy to know that someone's watching you.
A stalker can describe anyone who sneaks around, but it usually means a person who follows one specific individual obsessively. The word wasn't used this way until the early 1990s. Before that, it was mostly used interchangeably with "poacher" to mean "someone who pursues and steals game animals." The Old English word stelan lead to the English word steal, which is most likely the root of stalk.