Political History—focusses on great people, great political events (Thomas Jefferson or the signing of the Declaration of Independence). Can include foreign policy, memoirs/autobiographies, biographies.
Marxist History—focusses on the relationships between classes (the class struggle). Examines class in terms of revolution or change; oftentimes examines in terms of progress. (often includes economic history)
Annales School—great trends over long periods of time. Demographic changes, economic crises (the 17th-century had a "mini" ice age, consequent poor harvests and decline in population), the environment. Often uses geography to set the historical scene
Social History/The New Social History—takes much from both of the 1st two examples of materialism. Focus is on "history from below" or the history of everyday life. Special emphasis is given to shared lived experience, especially in recreating the histories of immigrants, women and minorities.
Cultural History—builds on revisionism of the materialist schools that focus on culture. Often uses language as a historical tool (the so-called 'linguistic turn'). Borrows from anthropology and linguistics to get at the mentalités of people in the past.
Intellectual History—often termed the history of ideas, this history early on examined great works, the 'classics.' Intellectual historians read these classics to understand the past and how people thought about their world (NB, Hayden White is an intellectual historian).