In the handbook of combinatorial designs by Jeff Dinitz and Charles Colbourne there is a table of symmetric designs. Is there a particular design or a particular type of symm design you are interested in? Symm bibd's are of great interest to me.
There are some tables about infinite families of symmetric designs as well as some sporadic ones in the monograph "Combinatorics of Symmetric Designs" by Y.J. Ionin and M.S. Shrikhande (Cambridge University Press, 2009).