Research demonstrating the effects of signing on hearing infants and toddlers:
A study done of children in childcare has found that hearing signing babies show less frustration and decreased aggressive behavior in childcare settings.
Grabmeier, J. (1999). Infants use sign language to communicate at Ohio State School. Newswise Press.

Research demonstrating the effects of signing on hearing preschool-aged children:
A study funded by the NIH demonstrates that by age 4, hearing children who used signs as infants and toddlers are linguistically and cognitively advanced, compared to hearing children who did not sign.
Goodwyn, S.W., Acredolo, L. P. & Brown, C. (2000). Impact of Symbolic Gesturing on Early Language Development. Journal of Nonverbal Behavior, 24, 81-103.

A study done at Pennsylvania State University of hearing preschoolers shows that even hearing children who are not exposed to ASL signs until the preschool years display literacy advancements over non-signing children. Specifically, they evidence enhanced vocabulary, spelling, and reading skills.
Daniels, M. (2001). Dancing with Words: Signing for Hearing Children's Literacy. Westport, Connecticut: Bergin and Garvey

Research demonstrating the effects of signing on school-aged children:
Follow up of the children in the NIH funded study reports that, compared to their non-signing counterparts, hearing second graders who signed as infants have an average IQ advantage of 12 points.
Acredolo, L. P., & Goodwyn, S.W. (July 2000). The long-term impact of symbolic gesturing during infancy on IQ at age 8. Paper presented at the meetings of the International Society for Infant Studies, Brighton, UK.