There are certain sections from the Torah that some communities have the custom of reciting each day. These include the verses in Parashat Ki-Tisa that speak of the Kiyor (the faucet in the Bet Ha'mikdash from which the Kohanim would wash); the verses in Parashat Sav that speak of the Terumat Ha'deshen (the daily removal of ashes from the top of the altar); and the verses in Parashat Tesaveh and Parashat Ki-Tisa that speak of the Ketoret (incense offering).
Sephardic custom, however, following the teachings of the Arizal, is not to recite these sections from the Torah as part of the daily prayer service. Although we recite the verses of the Tamid (the daily sacrifice in the Bet Ha'mikdash), and the section from the Gemara that discusses the Ketoret, we do not recite this section. (In some communities, the Kohanim read the section of the Kiyor each day.)
Many have the custom to recite the text called "Perek Shira" each day. This text speaks about the praises that the various animals sing to Hashem. Some women, in particular, recite a portion of Perek Shira each day, completing it over the course of the week, whereas others recite the entire text every day. The Sages teach that "Kol Ha'osek Be'Perek Shira" – "whoever involves himself in Perek Shira" – is guaranteed a share in the world to come, and will succeed in remembering the Torah that he studies. Notably, the Sages speak not of someone who "recites" Perek Shira, but rather of someone who "involves himself" in this text. To reap the benefits offered by Perek Shira, it does not suffice to simply mouth the words. One must understand what he is saying and reflect on the fact that even the animals give praise to Hashem – showing us that we, who recognize Hashem's greatness and kindness far more than the animals, certainly have the obligation to constantly give praise to G-d.