Electrolysis of water?

I want to separate the hydrogen from the oxygen. That's it. Just hydrogen and oxygen. Is there any way to do this using ONLY tap water? I've been trying to read around; it seems that everyone is saying that adding a soluble salt will act as a catalyst. Let's say I don't want a catalyst. Is this chemically possible, having the H2O being the reducing and oxidizing agent? So far, I've been using copper electrodes, although I'm not sure whether or not this has an effect. The reason I want only hydrogen and oxygen is because I want to do a little project, and from my experiments with dissolved NaCl, a green and brown solid forms at the bottom, something which I definitely don't want. Explanations with equations would be helpful. Thanks in advance.