Why do Mormons travel in pairs (husband and wife, two young women, or two young men) instead of a group? Does a pair that consists of a brother and a sister ever go on a missionary trip together?
There are many reasons why we send our missionaries out "two by two". First of all it was given by way of revelation to Joseph Smith that he should send out missionaries in this matter.
This command was also given by the Saviour himself when he sent forth his apostles "two by two" proclaiming his gospel to the people.
It is not always done two by two. If an odd number of missionaries are in a certain area, a group of 3 may be organized though not common. Fulltime missionaries will often invite regular members to come along with them on their visits. Fulltime missionaries are never permitted to evangelize by them selves. There are also many practical reasons for this. Safety being first and foremost.
The quick answer is that they do this for the same reasons other Christians engage in missions the same way. Paul talks about this in 1 Cor 9:
It all boils down to:
At its most basic, evangelizing in pairs builds in accountability, a mutual commitment to a shared goal, reinforced by the social pressure of knowing another human being is aware of whether or not you are adhering to your commitment. Additionally, there is a certain encouragement. As Ecclesiastes 4 says:
Even outside of LDS missions, just about every reputable missions agency has some form of accountability, in order to ensure that the missionary is adhering to his or her commitment.
Likewise, Mormon men and women do not go on mission together for the same reason that Baptist, Catholic, or other missions agencies tend to discourage opposite-sex missionary teams - namely doing so detracts from the mission. When, for example, the woman who would become Mrs. Affable Geek was a missionary in Nepal, she had signed a document stating that she would not date on the field. (True story: I never dated my wife till after we were married as a result, although we did "fellowship" alot!) The author of Hebrews alludes to this saying:
The distraction of trying to build relationship (not to mention the perils of losing your witness i.e. causing others to think that you were living in sin / having sex, even if you weren't!) is not conducive to the purpose for which you were sent. A husband and wife pair is different - they've already gotten through that.
Paul modelled this in his own journey -
As such, the LDS practice is both practical and Scriptural.
There are some good answers here that use scriptural references. You may find this chunk from the church's missionary handbook helpful:
Two reasons that weren't mentioned in any of the other answers are: (1) to keep them out of trouble, and (2) to protect them from false charges.
(1) Most of the missionaries are young adults, many of them younger than 20. I hope this this doesn't hurt anyone's feelings, but 18-20 year olds tend to be kind of immature and good at getting in trouble. It could be something as trivial as breaking into an out-of-use building and getting arrested. Things like this could be bad for the reputation of missionaries in general, give the mission president a headache, worry their parents back home, etc. In situations where missionaries are in a foreign country on a visa, things could be even worse. If there is another person with you 24/7, these kinds of things are less likely to happen.
There are also more serious concerns, and though the church tries to only allow people living in harmony with the church's beliefs to go on missions, sometimes people get through the application process who shouldn't have. Because you can't be 100% sure any given missionary doesn't have serious issues, even if you think you know them, it prevents some potential problems if they are in pairs.
(2) It is a general rule in business that you avoid being alone with clients to protect yourself from false charges, and because missionaries meet a lot of new people and meet with people in private settings (peoples' homes), they also adhere to this rule.
The following excerpt from the church's missionary handbook discusses missionary rules about staying together (when it says "companion," that means the missionary that you are working with):