While it is true that many mutations can cause problems for an organism, sometimes lethal, not all mutations are harmful. Most mutations are caused by single-point errors in the copying of a strand of DNA. For example, a strand of ATAGC may change to ATATC. This can have three major effects: a deleterious effect, a positive effect, or no effect at all. Deleterious effects, those which threaten the survival of the organism, will not accumulate, because they will kill the organism before it has a chance to reproduce. Conversely, mutations which cause no effect or a positive effect will accumulate in a population's genome. This is how Natural Selection works. It "selects" for positive changes in the genome, because only the positive changes will accumulate.

Certain mutations can add new, large pieces of DNA at a time. See this question on Gene Duplication for more information.