My God, Help Me to Survive This Deadly Love is probably the most well known graffito from the wall. It depicts the Soviet premier Leonid Brezhnev kissing on the lips Erich Honecker. (Note that this is an accurate representation of a photograph: Honecker and Brezhnev really did kiss like that.)
Today the remaining sections of the wall are covered in graffiti on both sides. However, during the working life of the wall, as the diagram posted /u/laughtolife shows, access to the East-German side was highly restricted. Here's a neat photograph showing the wall, the "death strip" leading up to its clean surface on the East-German side, and its graffiti-covered side facing an otherwise typical West-German street.
And slightly related: here's a photograph taken in Berlin in the 1950s, before the wall went up. The tension is incredible. The picture very clearly shows that once you're over the line, you're free. We typically associate this as East Germans gaining freedom from communism, but I love /u/Tychonaut 's comment about West Berliners being free from parking fines.
The Berlin Wall was constructed just before the border to West Berlin, therefore the 'western' graffiti side was technically east german territory. As such west german police didn't have jurisdiction over the 'western' side of the wall and DDR guards were busy literally looking the other way to prevent escapes from occurring. The space between the actual east/west border and the wall itself was wide enough to illegally park your car without west german traffic tickets and no noise ordinances. Because of this legal anomaly west berliners would party outside along the wall at all hours and was ironically the most liberating place in the world during the cold war.
At the 4:30 mark of this excellent short documentary about the Berlin Wall, it's shown how the Wall actually had doors that could only be opened by two guards, each carrying one key, so they could walk to the other side to inspect any damage.
"Walled In!" Germany's inner border: http://youtu.be/OwQsTzGkbiY
