I've always called it the dead fish shake, and I hate it.
To me a good handshake says "Hey there, I'm a solid person". The dead fish shake says "uhm, hi, I think, I dunno, what was the question again?".
I hate getting it from vendors, or most recently from contracts I'm talking with about renovations. And yes, I have to admit it does colour my impressions of them and their ability to do the work. I guess I figure if they have a so-so/half-***ed/wishy-washy handshake that they'll have the same attitude toward the work they're supposed to be doing.