Rabbi Avraham Hamoui, one of the Chachamim of the city of Halab in the late 18th-century, discusses in his work "Yemalet Nafsho" (Siman 9) several important Halachot concerning Tefillin (listen to audio for direct citation):
1) Based on the teachings of the Arizal (Rabbi Yitzchak Luria, Israel, 1534-1572), he writes that one should not remove his Tefillin after Shacharit until he completes the recitation of Al Kein Nekaveh Lach (the second section of the Aleinu prayer). The Shulchan Aruch (25:13) rules that one must keep his Tefillin on at least through the recitation of U'va Le'tziyon; Rabbi Chamoui rules that preferably one should not remove them until he finishes the paragraph of Al Kein.
2) He then cites the work "Shalmei Sibur" as advising that one not remove his Tefillin until he learns some Torah while wearing them, noting that "one will not earn the merit of acquiring his soul unless he learns with his Tefillin." This is one of the benefits of learning a Halacha each morning after the Shacharit service, as it ensures that everyone learns at least some amount of Torah while wearing Tefillin. It should be noted that those who wear Tefillin Rabbenu Tam should likewise make a point of spending some time learning Torah before removing them.
3) Rabbi Hamoui in this context warns against showing any disrespect towards the Tefillin, emphasizing that severe punishment awaits one who acts disrespectfully towards Tefillin. He mentions that one must avoid frivolity and laughter while wearing Tefillin, and that one may not bring them into any disrespectful place. He cites as well the Halacha forbidding holding the Tefillin by the straps, such that the box of the Tefillin is suspended in the air, as this constitutes disrespectful treatment of the Tefillin.
4) One must ensure that the Tefillin box be perfectly square. Sometimes, if Tefillin is frequently left in a hot car or worn with wet hair, the box can lose it square shape. One should therefore occasionally check not only the writing on the parchment of the Tefillin, but also the shape of the boxes, to ensure that they are perfectly square.
5) Finally, Rabbi Hamoui emphasizes the importance of properly observing the Mitzva of Tefillin, and writes that one who observes this Mitzva is rewarded with long life.
Summary: One must not remove his Tefillin before completing U'va Le'tziyon; preferably, he should not remove them before completing Al Kein Nekaveh and learning some Torah. One must avoid any kind of frivolity and may not walk into any disrespectful place while wearing Tefillin. One may not hold the Tefillin by its straps, such that the boxes dangle in the air. One must occasionally check his Tefillin to ensure that the boxes are perfectly square.
