Gemara

22b - Rav Yehudah: Sha'ul was punished because he pardoned his honor. "Base people said 'this one (Sha'ul) will not save us'; they disgraced him and did not bring tribute to him; he was silent." Afterwards, Nachash ha'Amoni came against Yavesh Gil'ad.

R. Yochanan: If a Chacham does not bear a grudge like a snake, he is not a proper Chacham.

Question: It is forbidden to take vengeance or bear a grudge - "Lo Sikum v'Lo Sitor"!

Answer #1: That refers to monetary matters:

Beraisa: An example of vengeance - Reuven refused to lend a scythe to Shimon, and the next day Reuven asks to borrow an axe, and Shimon says 'No, just like you didn't lend to me'.

An example of bearing a grudge - Shimon refused to lend an ax to Reuven, and the next day Shimon asks to borrow a garment, and Reuven says 'Yes. I am not like you, who refused to lend to me!'

Objection: Also regarding Tza'ar ha'Guf (e.g. verbal abuse) these are forbidden!

Beraisa: "V'Ohavav k'Tzeis ha'Shemesh bi'Gvuraso" - this is one who is disgraced and does not disgrace; people shame him and he does not answer...

Answer: A Chacham bears a grudge in his heart.

Megilah 28a: One of the merits to which R. Nechunya ben Hakanah attributed his long life was that he did not sleep before forgiving one who had cursed him.

This is like Mar Zutra, who would forgive all who wronged him before going to sleep.

Rishonim

Rambam (Hilchos De'os 7:7,8): One who takes vengeance transgresses the Lav of Lo Sikum. Even though he is not lashed, it is a very bad attitude. Similarly, one who bears a grudge transgresses the Lav of Lo Situr. As long as he bears resentment he is prone to take vengeance. Rather, he must erase the matter from his heart; this is the proper Midah that enables settlement of the world and interpersonal relations.

Kiryat Sefer: Mid'Oraisa, Lo Sikum v'Lo Sitor only apply to lending things. Regarding words or Midos, the Lavim are only mid'Rabanan.

Yad ha'Ketanah (De'os 7:17): If Reuven bothered Shimon in a way forbidden by the Torah, Shimon may hate him for this. The Torah commands not to bear the hatred in the heart, rather, to rebuke him, in order that the hatred will cease. But if Reuven did not transgress, Shimon has no Heter to hate him or rebuke him.

Rambam (Hilchos Talmud Torah 7:13): Even though a Chacham may excommunicate for his honor, this is not praiseworthy. Rather, he should ignore words of Amei ha'Aretz - "Gam l'Chol ha'Devarim Asher Yedaberu Al Titen Libecha". Great Chachamim praised themselves that they never excommunicated for their own honor. This is the proper attitude of a Chacham. This is when the Chacham was insulted in private. But if he was publicly insulted it is forbidden for him to pardon his honor. If he does so he will be punished, for this is a disgrace to Torah.

Rashi (DH d'Nakit): If someone else avenges an insult to a Chacham, the Chacham is silent.

Question (R. Chananel): The Gemara ignores "Lo Sisna Achicha bi'Lvavecha"!

Answer #1 (Erech Apayim, va'Yosef Avraham 1:22): Shulchan Aruch ha'Rav (CM Hilchos Ovrei Derachim 10) says that one subjected to Tza'ar ha'Guf may bear hatred. Also "Lo Sisna" is written regarding monetary laws, suggesting that it applies only to hatred for monetary reasons.

Note: Perhaps R. Chananel agrees with this answer; he merely asked why the Gemara does not address "Lo Sisna".

Answer #2 (Erech Apayim, ibid. DH v'Hinei): A Chacham must avenge without any personal benefit, like a snake that kills without intent to eat (see Anaf Yosef). Surely such a Chacham may avenge the insult to the Torah! The Gemara thought that it should be forbidden lest others think that he avenges for his own benefit. It answers that he bears a grudge in his heart, so there is no concern for Mar'is ha'Ayin.

Sha'arei Teshuvah (3:38): The punishment for Lo Situr is not for the words, rather, for bearing the grudge in his heart. The Isur applies only to grudges for monetary matters. One may bear a grudge for offenses of haughtiness, contempt and seeking to do evil. If a Chacham does not bear a grudge for such things like a snake, he is not a proper Chacham. If the offender requests forgiveness, he should forgive.

Rivash (220, citing Ra'avad): Kidushin (32a) says that a Chacham may pardon his honor. This applies to ways that others must show honor to him. If he was disgraced he may not pardon this.

Poskim

Shulchan Aruch (YD 243:8): A Chacham himself may excommunicate an Am ha'Aretz who disgraced him.

Question: In Yoma it says that a Chacham must avenge and bear a grudge, but in Megilah Chachamim praised themselves for pardoning insults!

Answer #1 (Beis Yosef Sof Siman 334 DH u'Mah she'Chosav ba'Meh): It is praiseworthy to ignore insults said in private. It is forbidden to do so if he was publicly insulted, for this is a disgrace to Torah. Rather, he should avenge and bear a grudge until the offender asks forgiveness.

Rebuttal (Bach DH Af Al Pi, through end of the Siman): No. The Tur first says that a Chacham may excommunicate for his honor, whether he was disgraced in private or in public. In either case it is praiseworthy to ignore it. Then he says that sometimes the Chacham may fully forgive the offender, even if the offender did not appease him. Then he says that this applies only if he was disgraced privately, but he may not fully forgive public disgrace until the offender requests forgiveness. We learn (Rosh Hashanah 17a) that if one overcomes his Midos, all his transgressions are overlooked. This refers to one who is not a Chacham, or to a Chacham after the offender appeased him. SMaG also says that a Chacham should be quiet if he was disgraced privately, but he may not fully forgive public disgrace until he is appeased.

Answer #2 (Ran, Rosh Hashanah 4b DH u'Mihu): If one pained a Chacham without insulting him, it is praiseworthy for the Chacham to pardon him.

Rema (7,8): Nowadays no one is considered a Chacham regarding the fine of a liter of gold for insulting a Chacham. Some say that nowadays a Chacham can excommunicate for his own honor; others disagree.

Source (for the first opinion - Gra 16): Tosfos (Bava Metzi'a 67B DH Ravina) says that Ravina did apply the laws of a Tzurba d'Rabanan to himself. All the more so we should not!