A general resume does not appeal to any specific employer. The objective statement gives you focus. It clearly communicates your interest to the employer. The career objective is the thesis statement of your resume. It helps to articulate the skills, experiences and education you will bring to the job.
Most employers find objective statements helpful.
Support your career objective statement with experience. A career objective must be focused to be effective. Omitting the career objective is better than using one that is vague or does not fit. Some combination of the above areas often results in an effective objective. You can have more than one.