Parshat Toldot, which teaches that Eisav was a hunter, is a suitable Parsha to discuss Halachic perspectives on hunting. We will focus on a celebrated responsum on this subject written by Rabbi Yechezkel Landau. Rabbi Landau is one of the עמודי הוראה, a pillar of Halachic decision making, whose responsa are characterized by brevity and penetrating insights into many Halachic topics. His responsum regarding hunting provides such insight into six Halachic topics. These include three Halachic prohibitions which he asserts are the basis for prohibiting hunting for recreational purposes.
Rabbi Landau begins by saying that recreational hunting would not be prohibited because of concern for צער בעלי חיים (causing pain to animals) because "there is no prohibition of צער בעלי חיים in case of human need." He cites Tosafot (בבא מציעא לב: ד"ה מדברי) as a source for this principle. Tosafot explain that even though it is Biblically forbidden to inflict pain upon animals, the Gemara in Avodah Zorah (יא.) permits severing the tendons of the horse upon which the king rode, because this is done for the honor of the king. The Rema (אבן העזר ה:יד) accordingly rules that "the prohibition of צער בעלי חיים does not apply in case of human health needs or other human needs." Rabbi Landau believes that since hunting serves a purpose of recreation it does not violate the צער בעלי חיים interdict. Moreover, he adds that only torturing a creature is prohibited but putting an animal to death is permitted. A significant group of Rishonim and Acharonim disagree with this assertion, see Rabbi J. David Bleich, Contemporary Halachic Problems III:512-712.
Rabbi Landau then asserts that recreational hunting does not violate the prohibition of בל תשחית, wasting, because "doing something that causes no loss to anyone is not a violation of בל תשחית." Moreover, one can benefit from the hides of the animals. Tosafot (שם) also asserts that the prohibition of בל תשחית does not apply in cases of human need. He explains that severing the tendons of the king's horse, is not considered בל תשחית because it is done to honor the king. Similarly, the Tiferet Yisrael explains that the individual in charge of those who guard the הר הבית could set fire to the clothes of a guard who falls asleep on the job (מדות א:ב) even though that destroys the clothes, because this is destruction for a purpose (disciplining the guard) and is not wanton destruction (see Encyclopedia Talmudit III:533-733.)
Rabbi Landau also writes that hunting as a sport cannot be considered "דברים המותרים ואחרים נהגו בהן איסור," something which is essentially permitted, but is regarded as forbidden by custom. This is because hunting (by Jews) is so uncommon that it cannot even be considered a custom. A custom cannot be established regarding an activity not commonly performed (see ש"ך, יורה דעה א:א for a discussion of a similar question, whether a custom can be established on the basis of what we see is not done - לא ראינו ראיה).
On the other hand, Rabbi Landau provides three reasons why it is forbidden to hunt as a recreational activity. First, he writes that it is entirely inappropriate for a Jew who models himself after Avraham, Yitzchak, and Yaakov to be engaged in a behavior characterized by the Torah as activities of Eisav and Nimrod. Rabbi Landau writes "How can a Jew can kill animals by his hands for no purpose other than for pleasure." Rabbi Aharon Lichtenstein explains that hunting is characteristic of the wicked because it is a means of procuring food, without having to wait, in a manner fraught with great danger. Hunting stands in stark contrast to agriculture in which hard work and patience are rewarded. Hence, we understand that hunting is an inappropriate act for a Jew to be engaged in (perhaps even professionally, according to this approach).
Rav Landau adds that one is prohibited to hunt because of the great danger involved in hunting (here he cites Ramban on our Sedra בראשית כה:לב). The Torah prohibits engaging in dangerous activities in דברים ד:טו where it states "ונשמרתם מאד לנפשותיכם" (and see ברכות לב:). Rabbi Landau, however, notes that if one needed to hunt professionally, one would be permitted to do so. This is based on a Gemara in Bava Metzia (דף קיב.) "מפני מה עלה זה ומסר את עצמו למיתה לא על שכרו" - which mentions (and implicitly sanctions) workers who engage in work which involves danger. The need to earn a living permits one to enter a dangerous situation, but for recreational purposes one is not permitted to engage in a dangerous activity such as hunting. Interestingly, Rav Moshe Feinstein (אגרות משה חושן משפט קד) permits one to be employed as a professional athlete despite the dangers involved (presumably, he is speaking about football or hockey) based on this Gemara. However, these responsa should give one pause before engaging in dangerous recreational activities such as hot air ballooning, white water rafting in very difficult conditions, and even skiing on a slope that is beyond one's ability to handle.
A third reason to prohibit hunting is that when one enters into a dangerous situation, one causes his sins to be remembered by God (ברכות נה.). This is because God must judge us to see if we are worthy to be redeemed from the danger. Hunting for recreation is hardly a good reason for us to cause our sins to be brought to Hashem's immediate attention.
Rema, (אורח חיים שטז:ב) writes that hunting is always prohibited because it is considered "מושב לצים," a frivolous activity. The דרכי תשובה (קיז:מד) cites שו"ת שמש צדקה חיו"ד ס' כז who adds that it is prohibited to hunt non-kosher animals to earn money, because of the prohibition to sell food which is Biblically prohibited (see שולחן ערוך יורה דעה סימן קיז).
We learn from these sources a vital lesson. We see that we must spend our recreation time doing constructive activities that are appropriate for the descendants of our illustrious אבות and אמהות. If we spend our recreational time involved in constructive activity, we follow the paths of our great ancestors, and we grow spiritually. Unfortunately, the opposite is true as well. We see that עשו is not entirely useless for us; instead he serves as a prime example to the Jews of behavior we must distance ourselves from.