Are there any alternatives to DNA as the hereditary material on Earth?
First of, depending on your definition of life (which is a matter of philosophy, not science) you may even accept as living something that has not heritable information passed onto 'offspring'. But let's consider only those hypothetical life forms who would have heritable information.

Of course, it is possible for different life forms to use some other mean of transferring heritable information. In fact, there are life forms based on RNA instead of DNA on earth (see RNA virus) and it is even thought by many that life first evolved using RNA and not DNA (see RNA world hypothesis).

To go further in this discussion you should have a look at wikipedia > Hypothetical types of biochemistry (I got the link from @RoniSaiba 's answer).