Many religious orders wear a rosary on the belt or cincture as part of their habit.
There is no official teaching, per se, about wearing the Rosary around the neck, but there are customs. In Irish-Anglo circles it seems to be frowned upon, as treating a sacramental as if it were nothing more than jewelry. In Latino cultures, on the other hand, rosaries are worn around the neck fairly often.
One problem is that it may be misconstrued if worn around the neck. So many gangsters, pop stars, etc. have worn it that way merely as a fashion accessory. In that case, it may cause scandal.
Like so many other things, it's a personal choice, being mindful that (1) it isn't a good luck charm; (2) if you're wearing it, your conduct should be above reproach; (3) it should be worn with appropriate piety and prayed often.
Might make more sense, though, to carry the Rosary in your pocket and wear a Brown Scapular instead. Rosaries are for praying -- Scapulars are for wearing.
Wearing rosaries is currently becoming a fashion statement for people who have probably never entered a Catholic Church. I assume the black Americans are picking it up from the Hispanic gangsters, who at least have a cultural connection with Catholicism if they don’t practice.
I’m thinking it must be a religious practice in Central America, because our Carismaticos wear them, mostly of wood, and they are mainly Salvadoran. The gangsters probably wear them as a badge of Salvadoran identity.
None of our clergy has said it is inappropriate for a devout person to wear a rosary around the neck. That would be going against history, since it has been done in various cultures throughout the world at different times.
AAM — most of the folks who blessed the Church, coming from the Episcopal community are “experts” — they put cradle Catholics like me to shame, what do you say, Mark?
"Sacred objects, set aside for divine worship by dedication or blessing, are to be treated with reverence. They are not to be made over to secular or inappropriate use, even though they may belong to private persons" (CIC 1171).
So, wearing a rosary if you really mean it as a personal symbol of prayer is ok, but as jewellery, no (no one is going to stop you and ask, unless you're a Goth! But even Goth's can be believers, right?)
I agree with AAM though -- a rosary is useful when it is carried in your hands, not around your neck.