What Does It Mean to Be Good?

I've recently had a few discussion about morality (some on Grundy's blog, some elsewhere) and it got me thinking. As atheists, we are often told that is impossible to be moral without God. If I point out that Atheists are often good people, a common answer I get is that without God you can do good things, but you can't be good. I would like to know what it means to be good if it is something other than doing good things.

If someone can do all of the things that (they think) God wants everyone to do, they why does it matter if they don't worship God? If you can have the same effect, why does it matter if the source is God or just your own personal morality? I think that Christians just think this is impossible. They are so brainwashed into thinking that we are all evil and deserve hell they they blind themselves to the reality that atheists can be just as good as anyone else. The more I write and the more I think about this, the more I find that particular bit of dogma disgusting.