Is one required to stand during the recitation of Kaddish?

The Rama (Rabbi Moshe Isserles, Poland, 1525-1572), in his glosses to the Shulchan Aruch (56, Halacha 1), writes that it is proper to stand during the recitation of Kaddish, and this is indeed the practice of the Ashkenazim, to remain standing throughout the entire recitation of every Kaddish. This ruling evolves from a comment in the Talmud Yerushalmi concerning the story recorded in Sefer Shoftim (chapter 3) of the judge Ehud Ben Gera. Ehud visited Eglon, king of Moav, and said to him, "I have for you a word from God" (Shoftim 3:20), at which point Eglon immediately rose from his chair. The Yerushalmi derives from this incident that it is proper to stand upon hearing the Name of God. Accordingly, the Ashkenazim make a point of standing during the recitation of Kaddish, when we give praise to the Name of God ("Yehei Shemei Rabba Mevarach…").

The Arizal, however, followed a different practice, standing during Kaddish only if he had been standing previously. (Pri Etz Hayim Shaare HaKadishim) This is, indeed, the custom of the Sepharadim, to remain standing if one had been standing before Kaddish, and to remain seated if one had been sitting before Kaddish. And, unlike the Ashkenazim, who remain standing throughout the entirety of Kaddish, Sepharadim stand (when they had been standing before Kaddish) only through the response of "Yehei Shemei Rabba…" (until "Da'amiran Be'alma"). (Halacha Berura, Helek 4, page 205)

Chacham Baruch Refael Ben-Hayim ruled that this obligation to remain standing during Kaddish applies even if the Chazan sings the Kaddish, as is common on Shabbat and Yom Tov.

Some Sepharadim have the custom to stand for Kaddish recitation during the Friday night service, in honor of the "Neshama Yeteira" ("additional soul") that envelops a person during the recitations of Borchu and Kaddish on Friday night. (Chacham Baruch Refael Ben-Chayim advised that one should make a point of standing at least during the recitation of Barechu on Friday night.)

It is improper to rush to one's seat immediately before Kaddish to avoid the need to stand during Kaddish. A person who is standing before Kaddish should not specifically sit just before Kaddish, but should rather remain standing. We must therefore question the practice of many people to rush to their seats on Friday night after the Chazan recites the Beracha "Mekadesh Ha'Shabbat" (at the conclusion of "Magen Avot") to avoid having to stand during Kaddish. (Ben Ish Hai, Parashat Vayehi, and Halichot Olam)

Summary: Ashkenazim follow the practice of standing throughout every Kaddish recitation, whereas Sepharadim stand only through the response of "Yehei Shemei Rabba" and only if one had been standing before Kaddish. Some Sepharadim have the practice to stand for Kaddish recitation during the Friday night service. It is inappropriate to rush to one's seat before Kaddish to avoid standing during the recitation of Kaddish.