The Talmud (Megillah 7a) notes that one of the proofs that Megillas Esther was written with ruach hakodesh (see Introduction) is that no human writer could possibly know that the Jews did not take any spoils.
Rashi writes that the Jews had rights to the spoils, but decided to wave those rights, and give the spoils to the king in order to maintain friendly relations with the palace.
The Dena Pishra writes that they did not take spoils because they did not want others to think that the Jews’ motivation was financial.
In M’aarchei Lev, Rav Moshe Schwab writes that since this was the property of Amalek, it was forbidden to take, as was the case for Shaul (Shmuel 1 15:3). and this is why the Jews refrained from doing so here.
In fact, the Binyan Ariel and Nachal Eshkol write that the Jews’ self-control in this incident was a tikun for the sin of Shaul in sparing (Shmuel 1 15:9) Amalek’s property.
Interestingly, the M’lo HaOmer and Me’am Loez both note that the initial letters of the ninth, tenth, eleventh and twelfth words of this verse, uvabeeza lo shalchu es (“and from their spoils they did not send”) can be rearranged to spell Shaul.
The Sfas Emes writes that the Jews took the spoils, but destroyed them in an effort to not benefit from the property.
However, R’ Yitzchak Yeruchem Diskin writes in Ohelim that Jews have an obligation to take the property of Amalek and destroy it, but did not do so here. The reason was that the Talmud (Megillah 16a) considers Haman to have been a slave. As such, he relinquished all rights to personal belongings. This includes his children. This also answers the question of how his grandchildren could study Torah in Bnei Brak if Amalek is never allowed to join the Jewish people. Such is not the case for his grandchildren because of his status of being a slave.
Megillas Seris adds another reason they did not take the spoils – they only had one day to kill Amalek, and they did not want to run the risk of missing the opportunity to fulfill this mitzva. In the course of performing a mitzva, they totally ignored anything ancillary to killing out their enemies.
The Gerrer Rebbe notes that matanos la’evyonim, the Halachic (Shulchan Aruch Orach Chaim 695:4) injunction to donate to the poor on Purim is in honor of the impoverished Jews of the time not taking the spoils of their enemies, despite their needs.
On the practical side, the M’nos HaLevi writes that one reason for Achashverosh to wait twelve months to have relations with the young women he had collected was to make sure first that they had no STDs or other illnesses. He needed twelve months for this, writes the Malbim, because there are some health conditions that are only apparent in certain seasons. After twelve months, they could be observed in all four seasons, and would thus be checked out and ready for the king.
Although we rightfully think of Achashverosh as an evil man, the Maharal notes that this verse demonstrates his self-control. Even a wicked man can have positive attributes. That, writes Maharal, is a kind of tznius, which is usually defined as modesty. Tznius is really a form of discipline, or self-control. In “A Canopy of Brocha,” a series of recorded lectures in which Rav Avraham Chaim Feuer discusses the Halacha of married women covering their hair, he points out that Hebrew word for “hair” (“se’ar”) is the same word as “storm.” In other words, reigning in and controlling hair is the real reason for covering it. This tznius, according to the Maharal, is the reason Achashverosh loved Esther (see 2:15 below). People love in another what they see in themselves. Even regarding the idea of “opposites attract,” the two parties involved like each other because they compliment each other.
Mystically, Rav Shneur Zalman of Liadi notes that these twelve months can be divided in two: one half for myrrh, and the other for spices. That being the case, he writes that the first half represent the half of our time on this world that we use meditating on the bitterness (“mar” means “bitter” in Hebrew) of life, and the other on the feeling of G-dliness (“bisamim” represent uplifting spices). It is indeed a constant battle to reach a middle ground between these two extremes. Our souls yearn for the spiritual world while our bodies are contented with the physical.
The Vilna Gaon proposes that this verse alludes to the idea that many things are allowed for a half and forbidden for a half a year, like intimate relations.
The Rema reads this verse as a reference to the fate of wicked people in Gehinom. There, the first six months are a time of extreme suffering, and the last six months are a time of easing up of that pain.