Board Thread:Questions and Answers/@comment-27612062-20160118002519/@comment-5014364-20160208183543

It's usually criminals these days, but as explained in the Night's Watch page, the original idea was that younger sons or bastard sons with little chance of inheritance would join up. The Watch is still considered honorable in the North, so Northern families are more likely to send second or third sons there.

Even Jon Snow wasn't "a criminal" - he volunteered because he didn't have much chance of inheritance.

Technically you're allowed to leave the Wall for formal meetings or whatever -- i.e. an officer going to a Northern castle to meet with a lord, particularly Winterfell the capital of the North. Most Watch members don't remember that much in contact with their family as Benjen - but if you're a high ranking officer and you're from Winterfell it's just a fringe benefit that you'd often have to go there on formal meetings and such.

In this specific circumstance, of course, Benjen wasn't just randomly visiting; the Watch heard that King Robert was going to visit Winterfell, which is very rare, and the Watch is desperate for more supplies and support, so they sent Benjen to try to plead their case to the king because he would be in the neighborhood.