What are the benefits and downfalls of delaying my child's vaccinations?

Weigh risk/benefit. There are no known benefits of delaying vaccines, but the risks of doing so are potentially severe or even fatal (e.g. Meningitis). One study in the journal pediatrics in may 2010 by drs. Michael smith and charles woods looked at children on delayed and traditional vaccine schedules. The delayed group did not perform better on any of 42 tests of cognitive, motor, and behavioral tasks.
Avoid Death/injury. We have been blessed by decreasing numbers of deaths due to illnesses like pertussis, polio, Hib meningitis & the like. Many parents assume since the other kids in the neighborhood get shots, her baby doen't need to. Well? Just assume that traveler from asia/south america/etc. Didn't get of a plane yesterday incubating that illness before brushing into you at the mall is it worth your babies life.
No benefits. Delaying your child's vaccinations will delay protecting your child from diseases that are waiting for them. That leaves them at risk. If your child is otherwise healthy, he/she should get them. No benefits in delaying vaccinations, unless your child has a fever, the flu, or a serious illness.