As far as I know, children whose mothers, auties or grandmothers are twins have a highher chance of having twins- fathers as far as I know are not a big factor- and it's your girlfriend's family who matters, yours will make no difference.
The female can inherit the trait of releasing two eggs in one ovulation, and if both are fertilised, bammo, fraternal twins.
Although, I guess she could inherit this from her father's mother. And sometimes, it just happens out of the blue with no twins anywhere in the family.
Identical twins are a chance occurance where an already fertilised embryo divides to create two seperate embryos. This is like lightning striking, it doesn't run in families, it just happens.
You would have to speak to a genetic counsellor to have your chancces assested, if you were trying to avoid having twins though, they's be able to work out the chances for you.
I might be doing that if we decide to have another baby after this one (our second) I don't want 4 kids, and my grandmother had 2 sets of fraternal twins!!!!!!! It would be typical to concieve two babies when I was only wanting the "last" one.