Are magic shows permitted according to Halacha?
The Rambam, in a famous passage in his Sefer Ha'mitzvot, discusses the status of "Ochazei Enyaim," people who perform tricks not through any type of alleged magical power, but rather through optical illusion and slight of the hand. This would include magic tricks familiar to us today, such as appearing to make objects disappear, pulling a rabbit out of a hat, and so on. The Rambam states unequivocally that the Torah forbids performing such tricks, and one who does perform this kind of magic is liable to Malkut (flogging).
Accordingly, Chacham Ovadia Yosef, in a famous piece in his Yabia Omer (vol. 5, Y.D. 14), rules that one should not involve himself in magic shows, or even hire a magician to perform before a Chatan and Kalla (bride and groom). He does permit hiring a gentile magician in situations of a Mitzva, such as to celebrate with a Chatan and Kalla; Jewish magicians, however, may not be hired even for the purpose of a Mitzva. He adds that anyone who participates in a magic show likewise violates this prohibition.
Rabbi Moshe Feinstein, in his Iggerot Moshe (Y.D. 3:44), discusses the question of whether it is permissible to consult hypnotists, who treat patients by putting them in a trance. Rabbi Feinstein writes that after consulting a number of hypnotists, he determined that hypnotism is a legitimate technique used to help patients overcome emotional problems, and does not involve any kind of alleged magical powers. Therefore, he writes, he cannot find any grounds for forbidding hypnotism. He does warn that a person seeking this kind of therapy must consult a Jewish, G-d-fearing practitioner. He then adds that although he cannot find any grounds for forbidding hypnotism, it is self-degrading for a person to allow himself to fall into such a trance. He therefore maintains that one should resort to this kind of therapy only if he indeed requires it, and not just for the experience.
Summary: It is forbidden to perform or participate in a magic show, or even to hire a magician. For the purpose of a Mitzva, such as to celebrate with a new bride and groom, one may hire a gentile magician. It is permissible to undergo therapy involving hypnosis in situations where such treatment is necessary.
