Why are organisms within a species genetically different?

1) Crossing over - in Prophase I of meiosis, non-sister chromatids in the same bivalent (i.e. chromatids on separate chromosomes within a homologous pair) can exchange alleles, creating new combinations.
2) Independent assortment - the random alignment of chromosomes in Metaphase I, and of chromatids in Metaphase II, means that random combinations of maternal and paternal DNA are brought together. For example, the maternal chromosome from pair A may be combined with the paternal chromosome from pair B. This process alone can produce 2ⁿ genetically unique gametes, where n is the haploid number.
3) Fertilisation - any sperm cell could fertilise a given egg cell, increasing the number of possible combinations of genetic material.
4) Mutation - random DNA mutations may occur during DNA replication (part of interphase). If the mutations are in the gametes, they will be passed on to offspring.