Some Twin Basics
Identical (monozygotic) twins are formed when a single egg, fertilized by a single sperm, divides. This often happens after implantation in the uterus, though the New England Journal of Medicine reports that it may happen anytime during the first 14 days after fertilization, resulting in the various forms of monozygotic twins. This type of twinning is not considered to be hereditary, although the cause of the division is not conclusively known.
About 0.4 - 0.5% of all pregnancies result in identical twins, accounting for about 1/3 of all twin births. Identical twins are always of the same sex (except in the case of Turner Syndrome, a very rare occurrence wherein the only variation is the X and the Y chromosome). Identical twins have exactly the same genes, while in fraternal twins, approximately half their genes are identical.
Fraternal (dizygotic) twins are created when two separate eggs released during the same ovulation cycle are fertilized by two separate sperm. The babies will not be any more identical than normal siblings, and boy/girl combinations are possible. This type of twinning is more likely to occur where there is maternal family history of fraternal twins. (Fraternal twins on the father's side? Doesn't matter -- the father's bloodline can't affect the number of eggs the mother releases. Who might it affect? Your daughter.)
When two eggs are fertilized by two different sperm from two different men, this is called "heteropaternal superfecundation" (HS). While such twinning is very rare, some speculate that it's actually a little more common than many people realize. DNA testing is required to determine paternity, which usually comes on the heels of suspicion that the mom had sex with at least two different men during her few fertile days.
Another type of twinning is still being researched, and results from a single egg splitting and being fertilized by two separate sperm.
Multiple birth statistics
Statistic source: Births - Final Data for the year 2000. (All figures are for the US only.)