This kind of common jargon has come to be expected. It would be impossible to remove it entirely without taking the "teeth" out of your CV or resume. However, if your cover letter is in English (I can't say for other languages), the language is flexible enough to be able to stretch these phrases through paraphrasing. Try transforming phrases using stronger adjectives and synonyms.
Hard worker becomes
tireless, driven <programmer, account manager, marketing associate>.
Team player becomes
dedicated to the success of my teammates, etc.
Someone who is REALLY reading your cover letter will see right through these tricks, but that person also won't care or might even take your letter a little more seriously because of the effort you've put into it.
In the end, it will be the skills and performance markers you list in your resume that will get the hiring manager interested in you. The cover letter is a nice lead-in to the real information, and it should be peppered with at least something that gets the hiring manager interested in seeing what lies on the next page.