I've heard it really depends on the quality/quantity of research you've done, because MIT wants really skilled researchers. I don't know, however, how that would differ from any other fine graduate institution. Maybe Mollie would know.
It does depend, very strongly, on the department for which you're applying. Graduate school is different from undergrad in that you're only applying for a specialized area of research, so asking questions about grad school only makes sense in the context of a particular graduate program at MIT.
It's generally easier to get into a master's program than a PhD program, at MIT or at any other top science or engineering graduate program. But the numbers can be misleading -- the aero/astro grad program admits about 50% of applicants overall, but a huge number of those admitted are former MIT undergrads, and almost 100% of MIT undergrad applicants are admitted (my husband's year, only two were rejected).
I would not use the fact that 19.7% of applicants to MIT's grad programs are admitted to argue that admission to MIT's grad programs is easier than admission to the MIT undergrad program. For one thing, a very large number of MIT grad students were themselves MIT undergrads (about 20% of each graduating MIT class goes on to grad school at MIT). For another, admission to top science and engineering grad programs in general relies on the applicant doing a number of things right during undergrad: pursuing interesting and meaningful undergraduate research and getting glowing personal recommendation letters from professors, to name two. Merely getting a 4.0 as an undergraduate and a good score on the GRE does not by itself make an applicant competitive in the least for top science/engineering graduate programs.
Generally science departments are less "inbred" than engineering departments. Science PhD applicants are generally encouraged to go elsewhere for their PhDs. Still, several of the science PhD programs (biology, brain & cog sci, physics) will accept MIT undergrads, even though they will counsel them to go elsewhere.
ChemE is the only engineering department, I think, which discourages inbreeding.
Physics and math are well-known at MIT for discouraging inbreeding.
Mollie's right that generally the science departments discourage it more than the eng departments. Brain & cog sci is a notable exception to this. It preferentially takes its own.
This illustrates the danger of using acceptance rates to determine how hard it is to get into anything - aero/astro has an acceptance rate of 45% at the grad level, but that's because it's very self-selected (a lot of the grads were MIT undergrads). If you had a representative population of aero/astro students across the country applying, they wouldn't get in at a rate of 45%.
The EECS program admits about 5% of those who apply. It is really spectacularly difficult to get into.
It also requires a minimum score of 7 on the IELTS, unless your first language is English, you have been been studying or working in the US for two or more years, or your undergraduate institution uses English as the language of instruction.
^ Thanks spratley. I want to figure out if I would enjoy and/or be good at doing research too. Do you have any idea how to gauge how someone might do in research besides having strong math/science backgrounds?