The following are some of the standardized exams that are required to gain admission in Bachelor, Master, and Doctorate degree programs in the United States:
For English Language proficiency, the most common tests are the Test of English as a Foreign Language (TOEFL) http://www.ets.org/toefl and the International English Testing System (IELTS) https://www.ielts.org/.
Some universities require admission tests for undergraduate and graduate level study to assess the ability and knowledge of the applicant. The most common tests for undergraduate applicants are the ACT https://www.act.org/ and the SAT https://www.collegeboard.org/. The most common tests for graduate applicants are the GRE http://www.ets.org/gre/ and the GMAT https://www.mba.com/.