Depends on where you're applying, actually.
I work for a large multi-specialty medical practice and the person who opens the mail dumps everything that looks like a resume or application into an "HR" pile, with one notable exception. If it says "NURSE" somewhere near the top (as is the case in an "objective" line), it goes directly to me for review. Those applicants don't get lost in a 'whatever' bin; the nurse manager (me) actually gets them promptly.
The "HR" pile gets looked at once a month or so, as they're only looking for clerical or MA spots to fill. If there's an actual nurse in that batch, it could be easily a couple of months before I get to see it. Resumes that had an objective line for a nurse? I get them fast.
As I mentioned to someone else, if your resume can in no way be construed as anything but a request to be reviewed for a nursing position, then fine--leave it off. But if you have a varied background, multiple degrees, a work history that is anything but "I'm obviously a nurse looking for a JOB as a nurse", then an objective might not be a bad idea. And in the case of my facility--a rather good idea. New grads often have just such a varied history--and one poor in nursing experiences-- on their resumes.