Answer:
Yes.
The factors behind monozygotic twins are largely unknown.
However with dizygotic twins, studies suggest that women with a family history may be more predisposed to twinning. Also women over the age of thirty, of a west African descent, larger women, women who have already beared children, those on fertility drugs and carnivorous women are all more likely to bear dizygotic twins.
There are two different ways a twin can occur:
Monozygotic twins: These are often referred to as "identical twins". This occurs when one egg is fertilised and then divides in to two embryos. They have nearly identical DNA.
Dizygotic twins: Often called "non identical" or "fraternal", this occurs when two eggs are fertilised and develop in to embyros. Apart from their age and their prenatal development, they can be very different genetically, be different genders, etc.