This is too big a topic to cover here.

Most prominent types: Racial or ethnic, gender, religion,

A 2012 Pew Research Center Report says that Three-quarters of the world's human population live under strong government curbs on religion, or among serious "social hostilities" involving faith issues, find researchers.
See TheGuardian.com

Here are some links.

Discrimination - Wikipedia,
Types of Discrimination in the U.S. Equal Employment Opportunity Commission (EEOC)
 Age, Disability, Equal Pay/Compensation, Genetic Information, National Origin, Pregnancy,
 Race/Color, Religion, Retaliation, Sex, Sexual Harassment 
 
American Civil Liberties Union (ACLU)
United Nations: Human Rights
10 Atrocious Genocides In Human History - Listverse
11 Facts About Religious Discrimination | Do Something

The MacBride Principles