One of my favorite gospels is Mark, and the early chapters of Mark are some of my favorite portions of the Bible. Here we find the conflict between Jesus and the religious authorities quickly and sharply defined, as Jesus regularly seems to break rules they find very important.
In the beginning of chapter 3, for instance, Jesus goes to the synagogue on a sabbath day and sees there a man with a withered hand. He calls him to the front of the synagogue and poses a question for the rest of the audience: Is it lawful to do good or to do harm on the sabbath, to save life or to kill? (Mark 3.4). Mark notes that the rest remained silent, and Jesus looked around at them with anger; he was grieved at their hardness of heart (v. 5).
What is fascinating to me at this juncture is the way Jesus poses the problem. He gives us only two options: either we do good or we do evil; there is no moral neutrality on the Lord's day. I would imagine that, in the context, his reference is to the man with the withered hand. Whereas Jesus intends to heal the man, they do not do anything for him, and through their lack of help they actually hurt him.
I think this is an important lesson to learn. So often we think of doing good for others as a kind of supererogatory "nice thing" to do every now and again, something we are not under an obligation to make the center and focus of our lives. But Christ's life is radically different from this, in that he was a man dedicated to others. He went about doing good and freeing all under the oppression of the devil (cf. Acts 10.38). His life is characterized by a constant and profound service to others (cf. Mark 10.45). He doesn't think that there is a neutral point between helping others and hurting others where you can coast most of your life; you are either in one camp or the other.
Of course we may not be able to go and heal others of their illnesses. We may not be able to teach others with great wisdom or give half (or more) of our salaries to the poor and needy. But certainly we can all do things like regularly pray for others, encourage one another upon meeting at church or in other contexts, etc. There is always something you can do for another person.