A close friend was stalked for years by someone who sent increasingly threatening e-mails to him, his ex-girlfriend, and her family with varying From: lines.
Local police in three different states were pretty sure my friend was the culprit because he knew a lot about computers. He got a restraining order and a pretty harsh interrogation; under the stress, he ended up failing out of university. The stalker got away with this stuff for years and never got close to getting caught.
The bad guy's mistake was to start sending e-mail with a "From:" line of a Department of Homeland Security agent. Turns out the FBI knows their stuff and does not tolerate this nonsense, and they unravelled the situation within about a week.
It also turns out that "impersonating a federal agent" is much worse than ordinary stalking — the bad guy is serving a 15-year prison sentence.
Anonymous stalking has always struck me as self-defeating. You want attention drawn to your existence, but don't want to admit who you are? How is that useful?
Because it could be anyone, knowing specifically who is harassing you leads you to understand the limits of someone's power (and giving you avenues of law enforcement escalation) versus driving someone batty with suspicion and mistrust.