Most graduate programs require the GRE (general test), which is more or less like the SAT.

A few--especially those more literature-heavy (and most PhD programs I would guess)--require the GRE subject test in English, which is significantly more difficult. If a program requires the subject test, that tells you something about it: that it values a background in serious literary study.

Click here for the GRE website which has a lot more information.

How important are the tests?

The general take on this is that many schools do have a minimum score on the GRE to apply, so you have to meet that minimum score. And if you do fantastically, it will help, especially when it comes to getting assistantships and fellowships (which are often awarded not by the department but by the school, based on GPA, GRE, and so on).

Should I study?

We don't recommend devoting huge chunks of time to it, but it's smart to familiarize yourself with the test format ahead of time. Maybe take a practice test or two. You can get a good study book, with practice tests and whatnot, for $20. That would be worth your while.