Evangelism -- What's the Point?

A few weeks ago, a man knocked on our door and asked if we knew Jesus Christ. Of course, I found it ironic that this person mysteriously appeared at our door on the same day we hung the Halloween decorations in the window, but that's beside the point. My husband assured the man that we were Christians. After all, my husband was a Lutheran pastor for 12 years, and I am still a Lutheran pastor and a religion professor at a Christian school. We go to church regularly, we pray before meals and at bedtime, we read the Bible, give money to charities, all that stuff that Christians are supposed to do, right? Well, it seems this was not enough. I wasn't the one standing at the door, but I heard the conversation get a little heated. Apparently, the man at the door didn't think we were Christian enough, or we weren't Christian in the right way. His concern was that we could be lumped in with the ministers he knew who would "go to the bar on Saturday night and then try to tell people how to live on Sunday morning" (his words). My husband assured him that we were on the straight and narrow (aside from the pagan Halloween witch adorning our door), but it took a door in the face to persuade the man that we were good Christians and to please leave.
This sort of door-to-door evangelism has always baffled me, particularly since I come from a faith tradition that doesn't do it much. My question is, What's the point? Are "evangelists" trying to save the sinful? Are they trying to persuade a person to adhere to the evangelist's own faith perspective? Are they trying to spread some good news about Jesus' death and resurrection and leave it at that? And, what if they run into people who already believe? What is the point then? In addition, why is it that that person hasn't been back at our door in over 3 weeks?
I say all this to get us thinking about Paul, the evangelist. Paul saw it as his mission to spread the good news of Christ to the entire known world, and for the most part he did. Over the course of about 15 years, he established Christian churches from Palestine to Rome. He endured suffering and imprisonment. He stood before numerous heads of government pleading his cause. He went from town to town, preaching, healing, and teaching about Christ. I'm positive that many people wanted to slam the door in his face, and I'm positive that many did, but he kept at it anyway. Why? Because Paul felt he had been called to this particular ministry by none other than Jesus himself. And, the thing to remember about Paul is that he didn't stop after he built a church. He continued to correspond with the people of that church and to help them through the persecutions they faced. These correspondences are the letters we have preserved in the New Testament.
My question to you is this: What is the purpose of evangelism? Even if we start from the premise that people can and do change their minds about what they believe, why is evangelism necessary? Paul obviously thought it was necessary, and without his efforts, I'm not sure where the Christian faith would be today. Keeping in mind that Christianity is one of only a handful of faiths that evangelizes at all, and that there are different types of evangelism (like service work or working with some faith-based non-profits) what is the mission? Do you think it works? In other words, can Christian evangelism today have the same effect that it did in Paul's day? Why or why not?