Should I share information about positions I have applied for with recruiters?
I recently put my resume up on Monster.com and a lot of staffing agencies have started contacting me to try and find me a job.
One thing they always ask me, in tones most benign, is whether I'm talking to any other companies besides the ones they've introduced me to. If I say yes, they ask which company (usually along with "Oh, I haven't even heard of them!" and I can almost hear them scribbling the name down), then ask how I found them, and who I spoke with there, and whether they're HR or technical or a recruiter, etc.
I can't think of any way it hurts me to give them this information, but somehow in the back of my mind I'm suspicious.
Is there anything I should know about this?