You should have asked them to mow your lawn; they would have happily done it. Then you might think to yourself, "
Gee, what kind of
wackos would do something like that?" You might also ask about their crazy religion and let them come in for a drink. Then we've got you!
The Bible actually says something about going door-to-door in it. Something along the lines of crying repentence unto every house, etc. Supposedly the Jehovah's Witness's take this extremely to heart and systematically hit every house they can, over and over again.
If a Mormon missionary is going door-to-door it means they have nothing better else to do. Their goal is to convert people to what they believe is the true faith. If all else fails they resort to this method. The Church has found that this method isn't very effective actually, even though it does occasionally yield a catch. Our missionaries try to focus on more effective methods like working with families in the Church to convert their friends/relatives, responding to requests for information or materials, etc. They will often also simply walk around a neighborhood talking to people working in the yards, or sitting on the porch instead of knocking on doors.
It's very important to note that, at least with Mormons, the goal of door-to-door proselyting is not to convert someone at the doorstep, or just to drop off some materials. The goal is to set up an appointment to have a personal discussion with them. The missionaries visit a person several times over the course of weeks with the goal of baptizing them. They also help them to find friends at Church, and answer any questions they have. They should (but don't always) continue to visit the person after baptism as well. I don't see how this would be a wrong thing to do. Mormons feel that they have the truth and that they have a responsibility to share that truth with the world. They don't (or, at least, shouldn't) take that to the extremes of forcing their views on other, or shunning people with different views.
A mission isn't necesarilly "required". It's not like you won't get into heaven if you don't go or something. The Church does encourage every male member (within some age range, 18-24?) to go on a 2-year mission though. It's very easy to show that a mission is almost always a positive event for a person. Beyond the religious benefits many missionaries learn foreign languages, develop much better communication skills, and are almost always put into leadership roles. Any employer who knows anything about a Mormon mission would count it as a bonus.
Wow, is this ever a ramble. I guess at some point I'll put together a coherent description of the Mormom mission.