Genetic variation is important because when conditions change (food becomes scarce, environment changes), some individuals in a population will be more likely to have variations that will allow them to survive. Those who reproduce pass their genes to the next generation. Variation helps species survive, and it's the reason species change over time.
In asexual reproduction, variation comes mainly from mutation. Mutation is a natural process that introduces permanent changes in a DNA sequence. However, microbes also acquire genetic variation through transformation, transduction, and conjugation (gene transfer). These mechanisms often come into play when conditions are harsh.
In sexual reproduction, variation comes from both mutation and recombination. Mutation creates the different versions (or alleles) of the same gene. Parental alleles are then shuffled—or recombined—during meiosis. Because of recombination, sexual reproduction produces more variation than asexual does.
Most commonly, traits are influenced by multiple genes and the environment. So for most traits, patterns of inheritance are complex and unpredictable. For instance, when a sexually reproducing organism inherits a defective or "broken" allele that codes for a non-functional protein, the second copy can often make up for the loss. This type of interplay between alleles, especially when traits are influenced by multiple genes, makes predicting inheritance difficult, if not impossible.
A small number of traits are influenced primarily by a single gene. Traits influenced mainly by one gene usually have predictable patterns of inheritance. However, most of the time even supposed "single-gene" traits are influenced by multiple genes, as in the case of eye color. And often times, a single gene can influence multiple traits. For example, some genes involved in eye color also influence hair and skin color.
In rare cases, changes in DNA sequences can cause disease. The pattern of disease inheritance can be predictable or unpredictable, depending on whether the disease is influenced mainly by one gene or by several genes. See Genetic Disorders
It's not quite accurate to say that everyone inherits two copies of every gene. In most mammals, the X and Y sex chromosomes determine whether an individual is male or female. Females have two X chromosomes, and therefore two copies of every gene. Males, however, have one X and one Y chromosome. For genes that appear only on the X chromosome or only on the Y (some do appear on both), males inherit just one copy.
Other living things have sex chromosomes too. Birds and reptiles have Z and W sex chromosomes. Unlike with X and Y, males have two Z chromosomes, and females have one Z and one W. Some insects and a few mammals have only an X chromosome. Females have two copies and males have one. However, sex is not always determined by chromosomes. With alligators, crocodiles, and most turtles, it's egg incubation temperature. And some fish can change gender in response to cues from the environment. Sex determination happens in many different ways.