The strength of the brickwork depends on a good brick bond. By brickwork bond we mean the over-lapping of the bricks, over that last 30-40 years stretcher bond has taken over from flemish bond as the most popular brickwork bond. The reasons are quite varied, but mainly it`s because stretcher bond is alot quicker, less wastage and less experience.
I have been a bricklayer  for 30 yrs and have never built a new house in any other bond than stretcher. I will list out the most common bonds for you and add other rarerly used bonds as they are requested.

Stretcher = brick in lengthwise
Header = brick in widthwise

            Stretcher bond: A bond that consists entirely of stretchers
              English Bond: A bond of alternate courses of stretchers and headers.
                Flemish Bond: A bond of alternate headers and stretchers.
                 Soldier Bond: Not really a bond, but this type of decoration is commonly used.