My admittedly-uneven stats as an admitted student:
GRE Score: 1270 (650 verbal, 620 quant, 5 analytical writing)...so not great. Only took it once because I decided to apply on a whim and didn't have time for a class or retakes. Would definitely not recommend trying this, esp. since I've been out of school for over 7 years
GPA: 3.87 (English education major w/art minor) + secondary single-subject teaching credential
Work Experience: 4 years teaching at a public high school + 2 summer school terms; 3+ years at an international ed non-profit (this was probably the strongest element of my application, as pretty much all of my professional experience is aligned to the programs I applied to)
Undergrad Institution(Public, Private, Ivy, etc..): non-premium medium-sized state school for undergrad, large non-premium state school for teaching credential
Research Experience: --
Applying for PhD or Masters: Masters
Program: Ed.M.
Schools/programs applied to & result: Harvard (TIE Ed.M.) & Stanford (LDT Ed.M.); got into Harvard, rejected by Stanford (suspect this was due to my sad, sad GRE scores?)
From what I can tell, it's pretty difficult to be able to accurately guess whether or not someone's going to get in to a program. I've seen a 50% acceptance rate figure floating around the board for HGSE; I suspect cost & awe probably keep a lot of people from applying. Harvard's amazing financial aid does NOT extend to masters students from what I can tell from my own offer and talking to other people (both at HGSE & at other schools). HGSE in particular says that they look at the whole student, which my admittance despite poor test results do seem to bear out.
I'd say apply to as many programs as you can afford to (what have you got to lose aside from the application fee?), but make sure you know why you're going and what you want to get out of the degree. Why do you want a masters in education? What do you plan on doing with it? Being able to tailor your SOP to how the program will help you meet your specific academic & career goals can only help. If I were going to re-draft mine, I'd probably take the time to name check specific profs whose research aligns to my goals.
Good luck!