The hygiene hypothesis proposes that exposure to infectious agents as a child in a sense vaccinates kids against allergies. The reverse statement is that adult allergies can be caused by being too clean as a kid.
In a recent study of 939 kids and their families, higher exposure to other kids as toddlers (but not as infants, which they define as 0-16 months) was associated with lower incidence of asthma at age 15. It was dose-related up to 9 kids; more kids = less asthma. After 9 kids, the effect reduced, suggesting a threshold.
So if asthma is a particular concern in your family history, you might be best off with small family child care, or a smallish large-family home, with a preferred capacity of 10 kids.