In answer to Mikey2573's question about Barrie's works having entered public domain in the US, the answer is yes and no: some have and some haven't. The Berne convention copyright term of author's life+70 years applies to works published after 1978. Barrie's works would fall into previous US legislation, whereby the copyright term starts from date of publication. Some of his early plays and novels would now be out of copyright, but not the later works such as Mary Rose or The Boy David where the Sonny Bono Copyright Term Extension Act apply, with a copyright term of 95 years from date of first publication. The Asquith family therefore still benefit from the Barrie legacy in the US.
In the UK (and the rest of Europe apart from Spain, another exception), all Barrie's works entered the public domain on 31 December 2007.
As far as Peter Pan is concerned, Alexander David is right in saying that the NOVEL is in the public domain (having been published in 1911 and not benefiting from the Sonny Bono Act) but the PLAY is still in copyright until 2023 (having been first published in 1928). However, I don't think this is the reason why the original play is less likely to be staged nowadays, because stage versions such as the Mary Martin musical, the current 360 Entertainment adaptation or even ballet versions are performed under licence by GOSH (or their agents).
My own feeling is that the play is rarely staged because audiences seem to expect something lighter and more 'fun' than the original, which is quite dark in places. In the UK, the pantomime and musical versions are also - sadly in my view - more popular than the straight play.
Hope this helps!