How can a Jew kill a living thing without any benefit to anyone and engage in hunting merely to satisfy ‘the enjoyable use of his time’? For according to the Talmud, it is permitted to slay wild animals only when they invade human settlements, but to pursue them in the woods, their own dwelling place, when they are not invading human habitations, is prohibited. Such pursuit simply means following the desires of one's heart.
In the case of one who needs to do this and who derives his livelihood from hunting (e.g., one who deals with furs and skins), we would not say that hunting is necessarily cruel, as we slaughter cattle and birds and fish for the needs of man....But for one whose hunting has nothing to do with earning his livelihood, this is sheer cruelty.
Sources: Rabbi Ezekial Landau Responsa Nodeh B’Yehuda, on Yoreh Deah 2:10, quoted Rabbi Joshua Telushkin, The Book of Jewish Values. Harmony/Bell Tower, 2000.