#Mathematica, 29 chars
    {s}//.l_List:>(l⋃##&@@(l/.G))

###Example:
    G = {1 -> {2, 3}, 2 -> {3}, 3 -> {1}, 4 -> {2}}; s = 1;
    {s}//.l_List:>(l⋃##&@@(l/.G))
>{1, 2, 3}