The half square triangle unit is probably the most commonly used patch in a quilt block -- well it is second only to the square. It is made simply with two triangles, filling up half the square each -- hence the name. Take a quick look through this website, or in any quilting magazine, and you will start to notice that this half square triangle, regardless of its size, is present in more quilts than not.
Free Quilt Block Pattern
The Rocky Road quilt block is a simple nine patch using only squares and half square triangle pieces. This quilt block can be a learning experience for a new quilter because the half square triangle pieces are not sewn into a square, but are attached to a small square to form a larger triangle, which then attaches to a larger triangle. This is a frequently used technique, and just goes to show that there are many ways to use half square triangles in your quilts. Small four patch "checkerboards" add some additional interest.
The obvious directional aspect of the quilt block also leads to using your creativity to come up with different layouts of the blocks. Ninety degree rotations can be used to create any number of interesting quilts. The illustrations below give you two such examples.
Similar Block ~ Jacob's Ladder
(As a side note, Jacob's Ladder was one of the quilt blocks used to leave secret messages in quilts made to assist escaping slaves along the "Underground Railroad" on their path to freedom. The book Hidden in Plain View: A Secret Story of Quilts and the Underground Railroad tells that story of how these quilts were used -- quite a fascinating read.)