Plain Weave  is the most simple weave pattern.  Both the warp and the filling threads/yarns cross alternately over one another to produce a stable, but less pliable fabric.

Basket Weave is a variation of the plain weave, this pattern consists of two or more yarns in the same alternating construction.  More pliable and stronger than a plain weave, but not as stable.  Commonly used in the composites industry.

Herringbone Weave  is a variation of the Twill Weave.  While the Twill weave is characterized by a diagonal ridge usually running from the lower left to the upper right,  the Herringbone variation has the diagonal ridge switching direction back and forth, creating a zigzag design.  One side of the fabric looks different than the other.  Often used to produce strong, durable fabrics. 

Satin Weave  has a characteristic luxurious sheen. The surface is composed of floats, or warp yarns, which pass over many filling yarns before intersecting cross threads at randomly spaced points to produce a smooth texture that appears unbroken.  This weave produces a fabric that conforms very easily around most contoured surfaces and is commonly utilized in the composites industry.

Leno Weave is used to create an open weave fabric.  A special attachment twists the warp yarns around each other in a figure eight as the filling passes through, imparting stability to fabrics with widely spaced yarns.