When I was in recruitment, one of the biggest 'fears' we had was that a really good candidate would get a counter offer from their existing employer and turn down our clients. All that hard work, phone calls, interviewing, coaching etc and then the number one candidate says NO!
Believe me when I say that many clients (let alone the recruiter) did not want candidate number two!
In fact we developed a whole strategy around the counter offer dilemma, even to the point of having a check box on the file - "Counter Offer Question Covered". There was one recruiter I knew of that even offered to resign on behalf of the candidate so the question never came up!
In the current market, where the talent shortage is even more acute you might well be in the envious (or NOT!) position of needing to consider the counter offer. I had it twice in my corporate career - first time turned it down and it was the right decision, second time took it and that was a bad decision (although eventually led me to do what I do now).
I wish in both cases I had some impartial counsel from somewhere (and believe me you will not get that if there is a recruiter involved - they are being paid by the hiring company so no way do they want your taking the counter offer).
If you are in that situation or expect it soon, check out this list of 10 tips to consider about counter offers that was posted on the 6 Figure Career Management blog by Sital Ruparelia.
Cross posted on the Reflections of a Square Peg blog.