I guess the trick is to put yourself into the shoes of someone who receives hundreds of cover letters every day. Ask yourself: if I was in that position, what would inspire me? What would catch my attention?
Here are some tips:
I once created a crossword-style cover letter when I speculatively applied for a creative job in a small organisation. Even though they did not have a job at the time, I had a reply from them within a couple of minutes. Unfortunately, they were not able to offer me a job, but I was quite surprised when two years later they got back to me and asked if I wanted to come over for an interview 
You could also draw a mind map on a flip chart and take a picture of it? Be creative! (CAVEAT: Think about whether a creative cover letter is appropriate for the job/ the role/ the organisation you are applying to. Don’t go over the top)
Include a very short personal statement that shows that you are passionate about the job. For example: “In my opinion, being a trainer is the best job in the world. I love sparking that “Aha!” moment in my learners!”
Instead of saying what YOU would like to get out of the job, let the potential employer know what you can BRING to the job. For example:” I believe your team can benefit from my [then list three things you are good at that will be of interest to the employer]“
Definitely customize your cover letter to the job you are applying for. Ensure the key words used in the job ad are repeated in your cover letter.
Don’t start each and every sentence with “I“. It sounds boring. Here are some phrases that you could use to not start your sentences with I: “In my opinion…”, “Working for… has given me excellent insights into…”, “Furthermore…”, “The key question, I like to ask is…”
Add something positive and unique about yourself. And never, never, never use the words “not” and “but”. Always talk about what you CAN do. If you are struggling with what you can do, then get a copy of Richard N. Bolles’ book “What color is your parachute?”. I bet it’s available at your local library. It’s an excellent resource and contains lots of exercises that will help you identify your transferable skills.
And finally, here is a link that takes you to many many examples of cover letters (hmmm… they can be a basis for your cover letter and they’ll need to be edited a bit to really make you stand out 
http://www.resumecoverletterexamples.com/
If you are looking for a job at the moment, there is more Free Advice for Jobseekers.
