Quidditch evokes several hypothetical problems in Jewish law (halakhah). Let’s briefly consider one hermercurial question: Is Quidditch a sport that is too dangerous to play?
First, let us stipulate that Quidditch is not a sport that is intrinsically violent and, in effect, set up as a controlled/disciplined way for people to hurt each other, like boxing. Boxing involves much hitting, predictable wounding and, reciprocally, self-wounding. It is plausible in Jewish law to forbid such wounding, even for entertainment and with mutual consent.  (The Maccabiah games have baseball, not boxing.) Nevertheless, there have been many Jews in boxing, including Orthodox (?) boxer Dmitriy Salita. [HT to this blog.]
UPDATE: Salita becomes first Jewish boxing champion in 30 years, HT Jew*school.
In Harry Potter, there have been serious injuries during Quidditch games -- but it’s no Roman circus (prohibited for spectators, too). Can we agree that injuries during Quidditch are incidental to the design and functioning of the game? Nevertheless, like many sports, Quidditch may lead to serious injuries. For instance, players could collide midair or otherwise fall to the ground. To analyze such sports, we might turn to Rabbi Moses Feinstein, the consummate American poseq (decisor).
R. Feinstein wrote a teshuvah (responsum) on the hazards of playing baseball. The teshuvah was published in 1963, when there was a real danger of getting “beaned” by a pitcher. Helmets were not required until 1971 and earflaps only later. Jewish major leaguers during this period included pitchers Ken Holtzman and Sandy Koufax. Anyway, R. Feinstein argues that batters can voluntarily submit to the chance of being beaned by a pitch in professional baseball. His cites one talmudic source: Bava Metzia 112 on Deut. 24:15. As an afterthought, R. Feinstein cites support for his position in a responsum of R. Ezekiel Landau (Noda bi-Yehudah 10) that permits hunting animals for the purposes of earning a living. R. Feinstein’s finding is based on two main criteria:
(1) Chances of severe injury. R. Feinstein assumes that the chance of serious injury in baseball is relatively distant (“one in several thousands”). Notably, R. Feinstein does not differentiate between harming and getting harmed (wounding and self-wounding). If it is acceptable for a batter to face 90+ mph fastballs, it is permissible for the pitcher to throw them. (That is, suicide and killing are both obviously forbidden by Jewish law… Reb Moshe does not comment here on the relative severity of either transgression.)
(2) Economic value of the activity. However, R. Feinstein gives his heter (permission) here for professional baseball only. A worker may consent to occupational hazards because they need to earn a livelihood (parnassah, which is commanded as a mitzvah).
How might R. Feinstein’s heter (permission) for professional baseball apply to school children and amateurs (cp. Quidditch)? (1) Reduced chance of harm. Ceteris paribus, school children would be prohibited from baseball. However, it is undeniable that school age children are not exposed to risks comparable to professional pitching. Furthermore, all baseball risks can be reduced by safety equipment. (Be sure your Little League is safe!) (2) Economic value of the activity. R. Feinstein quite likely would not approve comparable dangers for purely amateur sports. (Otherwise, why would he have limited his opinion to professionals?) Still, amateur sports might be condoned as comparable to professional baseball on various grounds. For instance, College and even Little League may be seen as a training ground for professional sports. Considering certain talmudic discussions, I believe that halakhah would permit apprentices and trainees to undergo reasonable occupational risks. [See my disclaimer if necessary.] In a more speculative vein, amateur sports may be seen as relevant networking (etc.) experience for earning a livelihood; if so, then R. Feinstein’s heter may apply to certain amateur baseball risks as well. (If recreational baseball is permitted by Jewish law.)
Now, what about Quidditch by school children at Hogwarts? (1) Chance of harm. I’ve only read Harry Potter books 1, 2, and half of 3, so far. Quidditch already has a track record of serious injuries, according to J. K. Rowling. However, the Quidditch injuries are mostly caused by outsiders (e.g., due to a spell or the appearance of Dementors). The game itself does not seem unusually dangerous. Flying, of course, is hazardous; in Harry Potter, though, flying falls within the halakhic category of a danger that is common to the multitude and acceptable because “The Lord preserves the simple” (cf. driving a car). In any case, the healing abilities of Madam Pomfrey et alia make up for the lack of safety equipment. So it seems likely that Quidditch is safer than professional baseball during the 1960’s. (2) Economic value. If Hogwarts is modeled on English schools, then sports offers training and networking for professional success. Furthermore, Quidditch is played professionally. Since wizards need to earn a livelihood, I’d argue that, from the standpoint of Jewish law, Quidditch adds sufficient economic value to justify its hazards even for amateur players.
(3) Caveat: informed consent. In his responsum, R. Feinstein emphasizes a key condition for his heter for professional baseball. All players must be playing of their own free will, with adequate knowledge of the dangers. If anyone plays Quidditch under duress due to Oliver Wood or the Dark Arts, then their exposure to the sport’s dangers cannot be condoned under Jewish law. By the same token, R. Feinstein warns that workers should not be running undue risks due to pressure by baseball managers and business owners. Occupational hazards without informed consent (MSDS's etc) are a non-starter.
For background on Quidditch, Wikipedia has a “project” on the Harry Potter books. Warning: The beauty of Wikipedia is that anyone can contribute. However, this allows vandals to put up unexpected spoilers. They get eliminated soon but you might chance upon one. Unfortunately, this happened to me today.
 On cosmetic surgery, R. Moses Feinstein reads Maimonides as forbidding wounding when it is derech nitzayon, contentious. Reading Maimonides differently, R. Eliezer Waldenberg apparently disallows harsh contact sports, without regard to contentiousness. Other halakhic sources on boxing here.
 Best quote: "If anyone wants a whupping from me, they got to wait until after sundown."
 See comments in Hirhurim here about Roman circus and misc about Harry Potter.
 Curiously, R. Feinstein does not mention who asked him the baseball safety question. Chaim Potok preparing for the opening of The Chosen? Seriously, does anybody know the circumstances the prompted this responsum?