Some say that the "Objective" line is the most misused waste of space on a resume. I disagree, but it does go without saying that if you're sending a pilot resume to XXX airline or flight department, your objective is to fly for them.
Each resume should be tailored to the specific employer. If the position that's open is MD-80 First Officer at Laxahatchee Express, then say that. Professional Objective: Employment as MD-80 First Officer for Laxahatchee Express. If you're applying for a government position, it's a good place to cite the vacancy announcement number.
I also believe in tailoring the resume to the type of employer. A utility operator isn't particularly concerned about your airline flying, perhaps, but may be very interested in past employment in the back country, or tailwheel experience, or maintenance experience. When I submit a resume for maintenance work, the employer isn't very concerned about my flying experience, but is interested in my mechanic background. The resume and the employment history should reflect what most accurately makes you stand out for the position you're seeking.
I've been hired at a job fair where numerous companies were recruiting pilots. When I attended the fair, I had resumes and cover letters personalized for each individual employer that I was targeting. When I was given my mini-interview, I opened a leather folder that contained my resume and cover letter, and presented it to the employer. The employer knew that I was attending to speak with multiple employers, but the employer only saw the one customized for them.
Remember that the resume and cover letter has only one purpose; to get you in the door; to get you the interview. That's all. It's also the first impression that the employer will have of you, and may be your only opportunity to be seen or heard. Until you have a chance to knock on the door for the interview, that resume IS you.