Any Disney 60 or 30 minute musical
The Musical Adventures of Flat Stanley JR.
Main restrictions: video recordings are for cast/crew/families only, can't be sold and can't be broadcast in any way including on the Internet.
The remaining shows do not allow videotaping. Parents cannot tape, even just for their own personal in-home use. It has nothing to do with how the tape would be used, not being sold, etc. It all comes down to legal copyright rights. Here is how Music Theatre International explains it:
Unfortunately, the rights to videotape are not available. Copyright law gives authors the exclusive right to control the reproduction of their work. When a license is granted for a live stage production of a show, that license does not include the right to tape it because the authors retain the sole right to decide when or if their work is recorded in any way. Even a videotape made for classroom use, as a personal memento or as an archival school record violates the authors' separate right to reproduce their work. In most cases, the authors have already granted such rights exclusively to film or television companies, in which case videotaping this show would also be infringing upon the rights granted by the authors to a third party.