If baby is at least six months old, the government's Advisory Committee on Immunization Practices (ACIP) says yes. Children age six months to five years are in the high risk category for flu complications, so immunization could literally be a life-saver.
Worried about mercury? You can check out the Centers for Disease Control and Prevention sitefor info on which flu shots do (and don't) contain thimerosal (the preservative in some shots that contains ethlymercury). According to the CDC, "There is no convincing evidence of harm caused by the small amount of thimerosal in vaccines, except for minor effects like swelling and redness at the injection site due to sensitivity to thimerosal," so don't freak out if the shot you're looking for isn't available. But do your homework and ask your docs about your options — the government anticipates plenty of thermerosal-free vaccines to go around for the under three set.
And, if your child is two-years-old or older, there's a new mercury-free alternative: the nasal spray vaccine, FluMist. The spray was previously only available to kids over five, but it has now been approved for younger tots! However, you should steer clear if baby has asthma or does a lot of wheezing — this one is not for those with respiratory issues.
Important note: If your baby is less than six months or has an egg allergy (talk to your ped if you aren't sure), skip both forms of the vaccine!