Most graduate programs require applicants to take an entrance exam as part of the application process. The following links will direct you to specific graduate level exams -
GRE - Graduate Record exam -- the most common graduate level entrance exam
LSAT - Law School Admission Test - exam required for entry into law school
GMAT - Graduate Management Admission Test - exam required by most business programs
MCAT - Medical College Admission Test - exam required for entry into medical school
MAT - The Miller Analogies Test - less common general graduate level entrance exam
TOEFL - The Test of English as a Foreign Language - used by international students applying to programs of study in the United States and is often used in place of the GRE.