I've been in both situation. I first encountered (2) when I was looking for my first fulltime job back in college. I had little idea of how much I'm supposed to get paid so I told the recruiter: "I had no idea how much I worth, but one day I'll find out. And if I realized I'm low-balled, I'll left for another company immediately and all the resource your company spend on training me will go nowhere." It worked for me. But I guess it won't work for those really sketchy recruiters since all they care is take their commission.

Little ballsy, Raises a good point as well. I'll need to keep that in mind when I go for my first FT job

Interestingly enough, recruiters get paid a % of the salary as a commission most of the time. This means they actually have an incentive to get you higher pay.

But they also can't keep bringing in people above a company's ask. It's a balance that has to be managed.

The biggest gap for the recruiter is between no and yes. The tiny increase they get for themselves for negotiating hard on behalf of their placement rounds to zero in most cases. If it costs them a placement, the opportunity cost is huge.

This is also often referred to as the "realtor problem", for those who've run into that one.

Point taken. For engineers, I can see this being the case.

I have always been in (1) or (2), but can think of (3) I'd love to be at this job (because of company mission, etc) . Maybe it is a subcase of (2)?

I think that would be a subcase of (1). Would be "give me what I want" which would be other reasons than "pay me what I want".

Absolutely, I should have phrased it that way from the start. I don't view salary as the end all be all, however I'll be the one to choose what I'm willing to take a discount for, not them.