Is there a proplem in the Halachic literature with hypnosis? What, if anything, is the issue involved in either hypnotising people or being the subject of such an hypnosis?
The Darkei Tshuva discusses it.
He quotes the Bnei Tzion (Siman 67) who was asked if one was allowed to do a procedure that he called "Magnetization", where one is put to sleep, and in his sleep the person would tell of events occurring far away, and of events occurring privately (in other words, Hypnosis). Being that according to nature it would be strange that such a thing could happen, the questioner wanted to know if this comes from "Kochos Hatumah" or not.
The Bnei Tzion answered that he asked scientists as to their opinion of the nature of Hypnosis. He reported that there were some scientists who said that Hypnosis is a fraud, and all that people see is their imagination. Others tried giving a scientific explanation, but admitted that they don't know how it really works.
In the end, the Bnei Tzion said that it is permitted because it is possible that it has scientific backing, and even though we don't know how it works, we may have just not discovered it yet. Moreover, one is allowed to be cured by a Non-Jew through magic as long as he doesn't use Idolatry, because it could just be a natural cure that we don't know about.
So he ends off that to be cured through Hypnosis is allowed, even if there is no danger. To do it for entertainment could be an issue, though.
The question also appears in the responsa of Rabbi Moshe Feinstein (Yoreh Deah 3:44 thanks blockhead), asked way back in the 1950s.
He writes that he spoke with someone who knows what hypnotism is; then consulted with Rabbi Yosef Eliyahu Henkin. Neither of them saw it as prohibited; the human mind is a complicated thing, and if using whatever mechanism works to help someone out, fine.
This assumes a person won't get hypnotized to do or believe something against Judaism.
However Rabbi Feinstein viewed the whole thing as somewhat degrading for the human dignity of the subject, so he didn't recommend it just for the fun of it. But if medically indicated (e.g. to quit smoking) or for some other need, it would be fine.
From Nefesh HaRav p233
"They asked our rabbi (R' Soloveitchik) if it is permitted for one to undergo hypnotism not for the sake of healing rather just for fun and games. Our rabbi answered that this is forbidden. Then they asked what sort of prohibition is involved in it? And our rabbi answered that is it "shtus" -- stupid -- and it is forbidden to be involved in shtus."