The most common standardized test you may need to take before applying to graduate school is the Graduate Record Examination (GRE).
You may also need to take a GRE Subject Test in one of eight disicplines, including psychology, English literature, biology and chemistry. Graduate programs in business require the Graduate Management Admission Test (GMAT) as do some other programs with an administrative focus.
You should plan to take any standardized tests early -- at least a year before you will enter graduate school.
Students considering joint degree programs with law or medical schools should keep the Law School Admission Test (LSAT) and the Medical College Admissions Test (MCAT) in mind and find out which tests are required by specific programs.