Much of the Book of Mormon describes a monarchic social structure. However, there is an interesting (from the social point of view) point where the government of the people switches over from a kingdom to a system of elected judges. Not exactly a democracy, but not too far away either.

There is a passage which I feel is applicable to people living in democracies today. The applicable section is in Mosiah 29, where King Mosiah is explaining how/why this new system could work:

[25]Therefore, choose you by the voice of this people, judges, that ye may be judged according to the laws which have been given you by our fathers, which are correct, and which were given them by the hand of the Lord.

[26] Now it is not common that the voice of the people desireth anything contrary to that which is right; but it is common for the lesser part of the people to desire that which is not right; therefore this shall ye observe and make it your law -- to do your business by the voice of the people.

[27] And if the time comes that the voice of the people doth choose iniquity, then is the time that the judgments of God will come upon you; yea, then is the time he will visit you with great destruction even as he has hitherto visited this land.

I.e., the reason a democracy can work is because usually the majority of the people choose good; but when they choose iniquity-- then watch out!

Personally I feel that this tells us it is at least as important for us to select our leaders based on their character, as it is to select them based on their policies.