Let's not fail to mention recruiters that cold call you at your place of employment, and are too dense to understand why you might possibly be upset at this.
Further I've never experienced a recruiter calling my current place of work (wouldn't he or she be fired?) and I often am and or can be vague re: where I'm actually working. Especially if you note you are working for some random govt. or contracting company.
Recruiters will still call the main company number and ask to be transferred to me. We're not a large place, so a receptionist physically takes the call. Oh yeah, she also serves as secretary for the VPs and our HR department.
And I still get email at my company address. We have a pretty standard first.last@company format.
I could choose to obsfucate my employer and location, but IMO that kind of defeats the purpose of keeping my profile current.
I've had two separate recruiters call my office, and openly tell reception they are calling "in regards to a job". I can only assume they Googled said workplace.
It could cause a strain in your current workplace and leave you more likely to need to jump - I find the whole premise incredibly offensive.