Details an applicant should include/exclude in an introductory letter to a prospective grad school adviser?
I have a list of things you should do from my seniors (Some might disagree):


Try not to over-sell yourself. There is a fine line between stating facts about yourself and boasting. Stay on the former side.
Try not to mention things and leave them abruptly or incompletely. For e.g., Don't say "I was involved with a project in the University of X where we studied Cancer Treatment." (Thats it). What did you do? Where did it lead? What is the status now? Thats the crux of the information and sadly, that is left out.
Have an interesting question or comment in the mail. Merely stating that you read a paper or attended his talk is not enough. Billions of other students will be stating the same. What made you like it? Why was it relevant to you?
Side note: Surprisingly, many professors who I mailed have been interested on how I stumbled on his paper.
Never ask direct questions that the professor wouldn't like answering (At least in the first mail). Asking him about his funding status isn't the best idea in the first mail. This is true for many reasons: For one, most profs wouldn't like telling you such details without you proving you are worth it (Why would they?). Secondly, your intentions are getting obfuscated. Are you really interested in the professor ( &amp; his research) or his money? If his research was interesting but he couldn't fund you for X years, would you still go?
If this wasn't obvious, don't mass mail/mail merge. 
Be honest about what you say. This includes no exaggeration.
Make it short. No one likes reading a billion lines to find out who you are.
Emphasize your work and what differentiates you from the rest rather than your grades and scores. Grades and scores (GRE/AGRE) are bonuses (or deal breakers) but they are secondary.