I tailor to the job. Your industry could be different but in white collar land separate formal cover letters are gone. You address the email or form (if from a job site) to a person if you can identify them. Always include the name of the position in the first para and subject. Make it very short and then put skills relevant to the job in bullets. Three sections. The bottom should point them to the resume and either let them know you would love to speak further. If it is popular to use linkedin do. Try to get you boss to write a ref on linkedin and coworkers too.

Example:

Recruiter/manager/hr,

I would like to be considered for such and such position that you have advertised on job site. I have x number of years in industry and excel at (some skill they are looking for). I believe I would be a great match. Highlights of my skills related to your requirements are:

Bullet one
Bullet two
Bullet three
Etc

Please see my attached resume for additional skills and qualifications. I look forward to hearing from you.

Modify it to your own style. Hr uses tools that search emails for keywords and if they are looking at 50 resumes having it short and sweet will more likely get you a call. It's also easier to Tailor to the job which will hold more weight.

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