To split hairs a little, I think you mean twins who look like each other rather than identical twins. Twins is the name given generically to multiple birth resulting in two children. They share a womb but can be genetically different.
Around one in three sets of twins is identical. This occurs because the fertilised egg divides in two while it is still a tiny collection of cells. The self-contained halves then develop into two babies, with exactly the same genetic information. Twins conceived from one egg and one sperm are called identical or 'monozygotic' (one cell) twins. The biological mechanisms that prompt the single fertilised egg to split in two remain a mystery. Approximately one quarter of identical twins are mirror images of each other, which means the right side of one child matches the left side of their twin.
Around two in three sets of twins are fraternal. Two separate eggs (ova) are fertilised by two separate sperm, resulting in fraternal or 'dizygotic' (two cell) twins. These babies will be no more alike than singleton siblings born at separate times. The babies can be either the same sex or different sexes, with the odds roughly equal for each.
Some researchers believe there may be a third type of twin, although medical opinion is still divided. It is proposed that the egg splits in two, and each half is then fertilised by a different sperm. This theory is an attempt to explain why some fraternal twins look identical.
One reason why film and programme makers do not use people who look alike is that it confuses the public. That's why everyone has a different first name and, in the US, they will choose characters for long running shows, eg. soaps and cop programmes, who look different. Two dark haired men in a programme will generally wear different coloured clothes if they are in the same scene for this reason.