1. MLA (Modern Langage Association) and APA (American Psychological Association), are the most common style formats for essays, reports and term papers. MLA formatting is used for papers based in the humanities (English, art, music, film, etc.) while APA applies to the sciences, psychology, and most branches of sociology.
Although there are more than a few differences between MLA and APA formats, the most significant is source notation—MLA requires citations, APA requires references.
This PDF lists the similarities and differences of MLA and APA: http://writingcenter.appstate.edu/sites/writingcenter.appstate.edu/files/MLA v APA 3-11.pdf
NOTE: Another format to be familiar with is CMS (Chicago Manual Style) which is primarily associated with history papers.