For the MA level: intellectual curiosity, independent thought, an interest in doing independent research (and a realization that that's what grad school is about).For the Ph.D. level: all of those things plus a doable research proposal and a good conception of which faculty members in our department can help them turn it into a successful project, and an interest in an academic career.
I'm a Ph.D. student. One thing our director of grad studies told me when I was interviewing was that if a program is your first choice and you would definitely go there if accepted, say so. It was, and I did, and I got in. I'm in the humanities, not sure if this would matter in the sciences.
The letter you receive should mention the same name of the graduate school as the one you work at. That will put you in the top 85% of applicants for my department.
I don't know, since I am never shown the applications or transcripts. I am going to start insisting, since my current M.S. student was sold to me as having a 3.96 undergraduate GPA, and it turned out he had a 2.96, with predictable results.
I've actually had students with low undergraduate GPAs do well in masters and Phd programs. They all had one thing in common though, they had grown up since then.
Yeah, well, my student illustrates how although one can't stop getting older, one can remain immature indefinitely.
He was also one of the "I'll do whatever you tell me to do" crowd. Shun those, because they lack the most precious resource in academia: their own ideas. Peter Feibelmann discusses this in his book, "A Ph.D. is not Enough": a letter of intent should describe what the writer wants to know, and how the writer thinks it can be found out in your program.
A 2.96? Phhhttttt. My undergrad GPA was lower than that. But my GRE's were great and I earned a 3.9 my first year as a grad student so I did OK. And yeah, it was growing up that did it. Basically my freshman and sophomore years were a total waste because I was having too much fun being away from Mom and Dad for the first time. My junior year I buckled down.
I look for evidence of initiative in pursuing the subject at a more advanced level than that required for an undergraduate degree: taking intro graduate courses, or successful involvement in a summer research program at another institution.Even better if the person show awareness of a current line of research that he/she finds exciting, and that is represented at my institution. (People's interests change, but at least this shows some specific motivation.)
I look for the arc of an intellectual life -- a set of questions and projects. People come to my discipline without specific projects in mind, and that's fine, but I look for a sense of how they got toward what they think they want to do through specific prior projects. "I have loved hamsters since I learned to hold a hamster" does not work for me.Also, that advice about declaring a first choice is brilliant, as where I work that might well yield you a fellowship (we lose the fellowship altogether if a student gets it but goes elsewhere, so it's in our best interest to nominate students for them whom we think will actually show up). Nobody seems to declare, though.