If my family has a history of ear infections, will my baby get them, too?

Not necessarily. The immune system is very complex, so there are many variables that will affect whether your infant will get ear infections. Most ear infections occur in the setting of colds- so one thing you can control is limiting your infants exposure to people who are sick and by practicing good hand washing.
Possibly. Research has shown that some infants are more prone to ear infections due to genetic factors, so these may "run in families". Even more important factors which increase the risk of ear infections are bottle feeding, being in daycare, and exposure to second hand cigarette smoke.
Baby look like you? While ear infections are not genetic, certain facial structures may lend themselves to predisposing you to fluid buildup in the middle ear, which can be a set-up for an ear infection. If you had lots of ear infections and your baby "looks" alot like you did as an infant, they may be more prone to infections. Big tip-avoid things like feeding lying down or exposure to irritants such as cigarettes.