The Gemara in Masechet Pesachim (113b) states that there are seven kinds of individuals that are excommunicated in Heaven and among them is one who does not don Tefillin on his arm and head, tie tzitzit to his garment, and place a Mezuzah on his doorpost. The Tosafot (ibid.) write that it seems that one must purchase a garment to tie tzitzit onto so as to obligate one’s self in the Mitzvah of tzitzit, just as we find in the Gemara in Masechet Sotah (14a) that Moshe Rabbeinu longed to enter Eretz Yisrael in order to be able to perform the Mitzvot that are specific to the land of Israel.
The Gemara in Masechet Menachot (41a) recounts that when an angel met Rav Ketina and saw him wrapping himself in a Tallit which was exempt from tzitzit (meaning a garment which did not have four corners, like most of our garments, which is exempt from tying tzitzit onto), he rebuked him and said, “What shall be with the Mitzvah of tzitzit?” Rav Ketina replied, “Do you punish for not performing a positive commandment in a passive way as well?” (Meaning that he was abstaining from performing a positive Mitzvah without actively doing anything.) The angel answered him, “Indeed, at a time of wrath and day of reckoning, we punish even for abstaining from performing a positive Mitzvah.” The Mordechi there (Chapter 541) writes that only when one has a four-cornered garment but looks for ways to exempt himself from this Mitzvah, such as rounding off one of the corners, is he punished for this, just as the angel told Rav Ketina that at a time of wrath, one is punished for abstaining from performing positive Mitzvot. Nevertheless, all this applied only to their times when they were accustomed to wearing four-cornered garments; however, nowadays when we are unaccustomed to wearing four-cornered garments, there is no punishment at all if one does not fulfill the Mitzvah of tzitzit and even during a time of wrath one will not be punished for this. Nonetheless, it is especially preferable to search for a four-cornered garment so as to be able to fulfill the Mitzvah of tzitzit.
Based on the above, it is clear that according to the opinion of the Mordechi, there is no actual obligation to wear a Tallit Katan with tzitzit tied onto it, for when the Gemara says one is punished for this, this applies only when one has such a garment and tries to exempt himself from this Mitzvah by behaving a crooked manner. However, nowadays when most of our garments are not four-cornered, one need not specifically wear a four-cornered garment in order to obligate one’s self in the Mitzvah of tzitzit. Similarly, the Rambam (Hilchot tzitzit Chapter 3, Halacha 11) writes: “Although one is not obligated to purchase a four-cornered garment a wrap himself in it in order to tie tzitzit onto it, nevertheless, it is not fitting for a pious individual to exempt himself from this great Mitzvah; rather, one should always try to be wrapped with a garment that is obligated in tzitzit so as to fulfill this Mitzvah. One should be extra careful with the Mitzvah of tzitzit during prayer, for it is a great degradation for a Torah scholar to pray without being wrapped in a Tallit. One should always be careful regarding the Mitzvah of tzitzit for the Torah equates this Mitzvah to be as great as all the other Mitzvot, as the verse states, ‘And you shall see it and you shall remember all of the Mitzvot of Hashem and you shall perform them.’” The Tur and Shulchan Aruch (Chapter 24) rule likewise.
The Gemara in Masechet Shabbat (153a) expounds the verse “Your clothing shall be white at all times” to refer to the Mitzvah of tzitzit. The Talmud Yerushalmi (Berachot Chapter 1, Halacha 2) states that one who is meticulous regarding this Mitzvah shall merit greeting Hashem’s holy presence.
The Sefer Chassidim (authored by Rabbeinu Yehuda HaChassid, one of the greatest earlier Rishonim) recounts that a certain individual had a dream that a deceased man came and told him he would die. Once, this man told him, “Confess, for you will soon die.” The individual would fast after every dream. During the dream, he would recite the Psalm of “By David, to you, Hashem, do I raise my soul” followed by reciting the entire Viduy (confession) in tears. He became deathly ill and saw before him a cloud in the form of a person carrying a load and holding a gold coin and the form of another man wrapping himself in a Tallit. He said, “In the merit of your wrapping yourself in a Tallit and the gold coin that you gave to a poor Torah scholar, you have been redeemed from death and you shall live.” He immediately perspired and was healed.
Thus, although there is no obligation to wear a Tallit Katan in order to obligate one’s self in the Mitzvah of tzitzit, nevertheless, it is very proper and befitting that every individual try to fulfill this dear Mitzvah which is equal to all other Mitzvot and to wear a Tallit Katan under one’s clothing all day. It is also proper to educate children regarding this precious Mitzvah and to dress them with a Tallit Katan ( the Sefer Eliyah Rabba writes that it is proper to dress a child with a Tallit Katan from the age of three and by doing so he will merit having a lofty soul).