What is the role of the MHC (major histocompatibility complex) in recognition of ?self?? For which?

MHC Class I Molecules interact with cytotoxic T cells. The target cell, in all situations, usually has some of the antigen inside of itself. The job of the MHC molecule is to bring a part of the antigen to the surface of the cell so the cyto-T cell can essentially destroy the cell. Without MHC, the antigen would never be presented and the cell would never be destroyed.

Class II molecules, on the other hand, interact with B Cells to complete its interaction. This MHC molecule does the same thing as the Class I Molecule.

Clarification from ametrine's answer...

MHC II does not interact with B-cells. After a B cells surface bound antibody has bound to an antigen it endocytosis it, digests it, and presents it on MHC II. This allows T-helper cells specific for a part of that same antigen to come by and activate the B-cell to differentiate into plasma and memory cells.

However, this interaction is not sufficient to activate naive T-cells, and is only one of the roles that activated T-helpers play. Naive T-helper cells must be activated by interacting with MHC II on professional antigen presenting cells such as dendritic cells or possibly macrophages.

Since MHC II is only present on several cell types it is not considered a self-marker, that role is designated to MHC I. While MHC I is required for T-cell activation, it plays another role in designating self with regard to natural killer cells. Natural killer cells are activated by cell surface carbohydrates, and are repressed by interactions with the glycosylations of MHC I. This means that natural killer cells are prevented from killing your own cells because of the presence of MHC I and also other non-classical MHC Ib molecules.