Yes. One example is the death of Michael Gartenschläger, who was shot in 1976.
Basically what happened was that he escaped over the East/West border, taking two SM-70 automatic-firing devices (http://de.wikipedia.org/wiki/Selbstschussanlage) (used on the border (not the Berlin Wall) in conjunction with mines) with him. He sold them to the German government, and was encouraged to go back in for a third device (which is totally crazy, in my opinion).
Gartenschläger is believed to have fired on two members of the Grenztruppen der DDR, who then returned fire, hitting him multiple times.
The guards were charged with his death in 2000, but were acquitted. In 2003, Stasi colonel Helmut Heckel and Stasi Lieutenant Colonel Wolfgang Singer (who oversaw the part of the border where the shooting took place) were charged, but also acquitted.
Another example is Peter Fechter, who was shot attempting to get over the Berlin Wall in 1962. He bled out in full view of hundreds of people in West Berlin, and his death was highly publicized. In that case, both guards involved in his death were sentenced to suspended twenty month prison sentences.
Yes, they were tried in court. There were more than a hundred trials known as "Mauerschützenprozesse". ("wall shooters trials.") You can find a judicial debate in english about it under the term "german border guard cases".