People join the Night's Watch because it is an honourable thing to do. Such people include Benjen Stark and Waymar Royce. The Starks have a long tradition of members in the watch.
As in the case of Waymar Royce, it is also a way for sons with no family inheritance to choose an honourable future that does not drain the resources of their family. Although this excuse has always seemed feeble to me, as children in age to be married mostly seem to be considered valuable, a way to strengthen the bonds between houses.
Lord Commander Jeor "The Old Bear" Mormont chose to join the watch so that his son Jorah could become lord of Bear Island. Similarly, Maester Aemon Targaryen joined the watch to forsake any claims to the throne, which then passed to his brother, Aegon V, the notable Egg, of the Dunk & Egg novellas.
The blacksmith Donal Noye of Storm's End joined the watch after losing an arm.
Ser Alliser Thorne joined the watch to escape execution for supporting the Targaryens in Robert's rebellion.
Mostly, one could say, it is a matter of honour, and of forsaking responsibilities or family commitments in an honourable way. In some ways, it is an option to death or suicide, to forever forsake life as a regular member of the realm.
As for benefits beyond that, you get food, clothes, work and a place to live, which may appeal to the poor.