A wealth of advice is available for students interested in applying to graduate school. This document does not replace that material, but I wish to add one brief piece of advice to MIT undergraduates.
MIT students who participate in the 5-year M.Eng. program have the option of applying to graduate school during either their senior year or their M.Eng. year. Either choice is reasonable. The former permits you to get an earlier start on your graduate studies as a regular graduate student (and slightly faster completion of your PhD — say, by about a semester). The latter gives you more time at MIT (experiences at multiple universities will teach you different things), and it gives you a stronger application (if you get a lot done during the extra year).
Whenever you apply to graduate school (senior year or M.Eng. year), I recommend that you apply at the same time to every program that you are interested in. Some students take a different and ill-advised tack, applying to MIT in their senior year, then to other schools in their M.Eng. year. There are a number of problems with this approach.
Most importantly, this approach prevents you from seriously considering your options, by not placing MIT on an equal footing with other schools. Think about why you are applying to graduate school: surely there are other places than MIT that would let you achieve those goals. If you haven't considered them, then you probably haven't seriously considered what you want to do and why you want to go to graduate school. (Staying at MIT for an M.Eng. degree out of inertia rather than as a reasoned choice is bad; but staying for a Ph.D. for the same non-reason is terrible.)
Some students plan to apply to MIT during their senior year, then apply to other schools (or to MIT again if they are not accepted) during their M.Eng. year. This is bad even if you do get into MIT, because you might become so comfortable with the default of staying at MIT that you don't seriously consider other options. To accept admission to the MIT Ph.D. program with the intention of (seriously considering) leaving after a year to go elsewhere is deceitful: don't pursue such an option. This is bad because if you don't get into MIT during your senior year, you run the risk of seeing the others as second choices. If you reapply to MIT, you must disclose your rejected application; it can't be a positive (though it isn't an insurmountable negative). You don't want to prejudice the committee members or to have to work extra hard to show what has changed.
The upshot of all this is that you should decide:
Don't instead make the following, more convoluted, pair of decisions:
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Michael Ernst