You can, but it will not be very effective. When you use the same letter for all positions and employers, it reads like a form letter and it is not very convincing. It says: "I am looking for any position with any company." Employers want to hire people who are excited about working for their company and who will love fulfilling their requirements. Form letters can rarely communicate your interest or excitement as it pertains to a specific situation. The extra effort will reap more interviews. 

The goal of the cover letter is to highlight your attributes and orient an employer to your resume. The content of your letter needs to be specifically tailored to the needs of the company and the position. You need to stand out from the crowd. The best way to do that is with a personal touch.