Professional organizations provide learning and networking opportunities to help you stay current in your field, as well as make connections with colleagues. They often are publishers of journals, books, and other works about the profession. Guilds are also common in the entertainment industry, and are somewhat in between a labor union and a professional association.
Some more general organizations are listed below; others are grouped by topic/discipline in the other tabs. This is not a perfectly exhaustive list but will help you get started exploring the possibilities!
Don't see one for you? Just try searching online for [instrument] professional organization.