APA (American Psychological Association) - used in the social sciences

• Recommended - Purdue OWL APA Style - Includes a tutorial for citing in APA style as well as sample papers and bibliographies.
• Frequently Asked Questions about APA Style - Official APA style site containing tutorials and other FAQ's.
• APA style blog - Need help citing a odd source or a sample paper? Check out the official APA style blog.

Chicago Manual of Style - used in the humanites and social sciences 

• Recommended - Chicago Manual of Style - Official online version of the Chicago manual 17th edition.
• Recommended - Purdue OWL Chicago Style - Includes a tutorial for citing in Chicago style as well as sample papers and bibliographies.

MLA (Modern Language Association) - used in literature and the humanities 

• Recommended - Purdue OWL MLA Style - Includes a tutorial for citing in MLA style as well as sample papers and bibliographies.
• Recommended - The MLA Style Center - Official MLA style site, containing tutorials and other FAQ's. Updated for MLA 8th edition.