I read the first book in the series and started with the second. So far, I noticed that, although northern noblemen are much more willing to join the Night's Watch, there was a healthy number of southron lords among them as well and some were even volunteers.
However, among them, the name Lannister was oddly missing. Somewhere at the start of the second book it was explicitly said that Lannisters were never friends of the Night's Watch, which would also mean that taking the black wasn't really a common thing for them to do.
"If the winds have been kind, Ser Alliser should reach King's Landing by the turn of the moon, but whether this boy Joffrey will pay him any heed, I do not know. House Lannister has never been a friend to the Watch."
A Clash of Kings, Jon I
On the other hand, there is an exception to everything. For example, Tyrion could be called a friend of the Watch. Was it ever mentioned in the rest of the books if a Lannister ever joined it?