Well, it could be a component of full-blown stalking.
It could also be a way to keep tabs on, say, a dead-beat dad who owes child support.
Or hook up with former classmates or friends.
Or track what your grandkids are doing.
Or fixate on a celebrity instead of living your own life.
I had a really interesting conversation with a co-worker many years ago. A mild-mannered geologist, friendly enough guy, he said he'd gotten fixated on a woman he was interested in and starting doing stalker-like behavior. He noticed and stopped doing it, but it struck me as unusually insightful and self-controlled to pull back from the edge - like that rare alcoholic who can quit without hitting bottom.
I can imagine someone googling an old flame some lonely night or after a fight with their spouse. But if they put a Google Alert on them, then the hits will just keep coming back to them, when they weren't otherwise thinking in that vein. Generally I'm all for more choices, but this does seem like it could be destablizing for some people (on both sides of such an alert).
Is there a way to know who has put a Google Alert on you? Probably not. If you turn up dead someday, can the police get a search warranty to find out? Hmmmm.