Yeah, many were killed evidently trying to cross.
Here's one of the more famous deaths:
Peter Fechter (January 14, 1944 – August 17, 1962) was a German bricklayer from East Berlin in what became East Germany in 1945, who, at the age of eighteen, became one of the first victims of the Berlin Wall's border guards while trying to cross over to what was then West Berlin.
Fechter supposedly was shot in the hip, stumbled into the barbed wire, became entangled and bled to death while both American and German/Soviet soldiers had a standoff as to who would help him.