One of the earliest -- and perhaps the most wide taught -- models of dividing personality was Freud's division of the mind into the id, ego, and superego. A good place to find out about the id, ego and superego is at Victorian Science. The essay there is by David B. Stevenson.
Another kind of personality structure involves divisions of personality based on the functions they carry out. One of the most promising of these functional divisions is the Systems Set, which is described in part on this web site -- click here to pull up the special topic.