"My fellow Americans, ask not what your country can do for you, ask what you can do for your country."
- John F. Kennedy
It's a profound and famous quote about the responsibilities that come with citizenship, but it can also be applied to job searching by changing a few key words: "Ask not what the company can do for you, ask what you can do for the company."
So what does mean? It means that if you're writing your cover letter all about why you want to work at that company and what you hope to gain you're doing it wrong. Sure, HR people want to know you are genuinely passionate and excited about the work that company does, and you should showcase that. However, hiring managers are looking to find a person with a solid track record of real results. They want the people that can get the job done, improve profits, refine systems to save time or money, and help the company to grow and improve. The best cover letters are the ones that tell them how you will do that.
Does the job call for social media skills? Great, tell them about the tweets you sent for a business that got 50 retweets and 35 favorites. Do they want someone with experience in PR? Tell them about the feature you secured in a local paper. (Don't make these things up, these are just examples.) Think about your work history and experience and how it applies directly to the job you are applying for and tell them how you have already used these skills to help grow or improve a business.
So stop writing cover letters thinking about why you want this job so badly and start asking yourself what you can do for each company.