Robustness is probably one of the most important priciples in software development.  Even more important than Security or Reliability.
The reason is simple.  If the software is not robust then it can not be secure nor reliable.  Robustness indicates how well the system's other features perform their function and continue to perform their function.
Robustness is a principle and not something you do, if you copy what someone else does to create robust code, you misssed the plot.

Below are some articles on robustness, learn from their thinking process and not from their lists of things they do to improve robustness.
Alberto Gutierrez has a good set of 10 characteristics to learn from.
Matt Bishop's robust programming article.
You may draw a robustness diagram to see all the potential fragile points in your system.
Read more on how robustness is often overlooked or wrongly called "quality".
iMatix tells how they build reliable/robust systems.