Many people wear and worship a cross to symbolize their devotion to God. I think that a circle is a far more powerful symbol. Indeed, the Celts seem to have come to the same conclusion, as Celtic crosses incorporate both a circle and a cross.
A cross symbolizes conflict. It's a constant reminder of a past wrong done to one group of humans by another. It's a constant call to arms. Indeed, the cross symbolism in Christianity is strongly related to the swords of the Crusaders, who went out and spilled all sorts of blood in the name of religious right. But doesn't the Bible also say that Jesus said to turn the other cheek? If he was alive today, would he be delighted to see all the people killing each other in the name of religion? I think not.
But a circle gives us no license for violence. 
It reminds us that we are all one, a constant reminder that everything we do will come back to us.
That's everything we do to another human being, every action we do to our environment, everything we do in our own lives. Since we are all part of an unbroken circle, pulling on any one part of the string affects every other part.
Since I believe this, I actually feel kind of pleased if I realize that I've dropped some coins, because I automatically think of the positive side -- another person will be so happy to find them! Likewise, though, I believe that if I were to do something to deliberately hurt another human being, that would hurt myself.
If everyone chose to act with a deep awareness that everything they do that affects others, affects themselves, and truly helped others live each day they way they want to have their own days, the world would be a better place. Of course we all need to set our boundaries, but we do need to get rid of the mistaken notion that we can somehow act and let others take the consequences. It might work like that for you short-term, but not long term.
Writing this, I realize that a cross as a symbol might work if one visualized it as a sign of meeting paths. If every time you thought of the cross you were wearing, you thought that when you met a fellow traveller at an intersection on Life's Journey, you would treat them as Jesus said to -- treat them as you want to be treated. Treat them with compassion and dignity and kindness.
And treat them like another being who is one with you. Treat thy neighbour as thyself, because thy neighbour IS thyself.