One of the most popular designs is the root-over-rock design where a tree or trees is growing draped over a stone.
In this example a Ficus ‘Mystery’ was placed on a rock about 9-10 years ago. It was a piece of a larger plant see http://www.bonsaihunk.us/info/BreakingUpIsEasyToDo.html
This section was frankly quite ugly and I almost discarded it. Rather than throwing it away I decided to place it on the rock. It was strapped to the rock with plastic tape and grown for years with most of the rock and the roots buried in soil. Over time the roots and the stone were exposed.
You can see the result in 2014. The bonsai has improved dramatically and one day may become one of my favorites.
Root-over-rock designs can be done in many ways but the best and quickest results will be achieved with plants that have super aggressive root systems. Plants that grow slowly and have fibrous root systems generally will not succeed as root-over-rock designs.