Here are some wonderful theatre companies that offer Apprentice Programs and other exciting opportunities to new and experienced actors. These are great ways to stretch yourself outside of school, learn new techniques, and make great new connections in the industry. If you know of others I could add to the list, let me know!
Actors Theatre of Louisville
Williamstown Theatre Festival
Walnut Street Theatre
Great River Shakespeare Festival
Specialized Conservatory Programs
British American Drama Academy
American Conservatory Theatre
Shakespeare Theatre Company
Summer stock is a whole other list I'd like to eventually add.
The truth is, it's difficult to find apprenticeship programs anymore. Apprentice positions used to be the way an actor could work their way up in a company, and now collegiate theatre has relegated apprenticeships to the bottom of the totem pole. There is a movement to bring the apprentice style program back as a training technique because it gives actors a foot into an established company, allows them to work side by side with professionals, attend rehearsals and master classes with the actors of the company, and is a more realistic approach to learning how a company is run (both as a business and artistically). Many believe that collegiate theatre is killing American theatre by allowing too many students into the fold, and graduating more actors than there are jobs to place them in. These actors range from under-trained to badly-trained, and many are trained in such a cookie-cutter fashion that they do not fully comprehend the differences between collegiate theatre and the real world. This is the reason so many graduate programs have become selective, some going so far as to only accept a new class every three years.
I digress. It is a complicated matter that I don't fully understand but plan to learn much more about. American Theatre is in limbo, and it's up to the next generation of young artists to decide which way we'll fall.