Much of the genome of any species is in what are called ``non-coding'' regions. These are sections of the DNA strand that might be there for structural purposes (e.g. to help fold the strand into its familiar double helix shape), or simply in sections that do not code for any function.
If a mutation occurs in a non-coding region then it will likely have little or no effect. Even if it occurs in a coding region -- for example a region that contains codes for amino acids used to build vital proteins -- it might not have an adverse effect. For example, a substitution that turns CUU into CUA in an RNA molecule will have no effect, since both are codes for the same amino acid (leucine). Mutations that do have an observable effect may lead to very minor changes in the organism -- e.g. blue eyes instead of brown -- but they could also be lethal -- for example a fatal allergy to a common food source.
It is possible a mutation could be favorable, for example sharper visual accuity that makes a predatory animal a more effective hunter. In general, however, the vast majority (97%) of all mutations are either harmful or neutral.
If a mutation occurs in a recessive gene it may not be expressed, i.e. the effects of the mutation will not be seen. In these cases the mutation is carried in the genes of the individual, and may be passed on to successive generations, only to show up as a harmful mutation in a later generation when an individual with homozygous recessive genes is produced.