Someone commented to me that the desire for revenge is not a healthy one. This is only partially true. Like all midot, revenge has its proper place in life. When it comes to our enemies, revenge is an important tool that must be used to restore the Honor of Heaven. The Jewish people are Hashem's representatives in this world. Those who seek to hurt us, seek to hurt the Kingdom of Heaven. I will just bring a few sources to show that revenge in its proper place (against our enemies or the wicked) is a great thing:
Chazal say (Brachot 33a):
... Is revenge truly a great thing since it was put between two [names of Hashem] "Hashem is a vengeful G-d"? He answered: "Yes, in its proper place it is a great thing."
Rashi comments on this gemara: "In the place where revenge is needed, it is a great thing."
Chazal interpret this very verse as describing Moshe Rabbeinu's desire to see vengeance before he dies (תנחומה מטות ד): "Moshe yearns to see vengeance against the Midianites before he dies and requests from Hashem that he should see it with his eyes."
Chazal use this episode to teach a general lesson about the place of vengeance in Jewish life (ספרי מטות קנז): "'And Hashem spoke to Moshe to say: Take the vengeance of the children of Israel from the Midianites ... And Moshe spoke to the nation to say: Prepare for yourselves people for an army and they will be on Midian to deliver Hashem's vengeance on Midian.' (במדבר לא:א-ג) This is to tell you the praise of the righteous that they do not depart from the world until they avenge the vengeance of Israel which is the vengeance of He Who created the world.
The vengeance of Israel IS the vengeance of Hashem!
Chazal say this even more explicitly in a different place (ספרי בהעלותך פד): "'Rise Hashem and your enemies shall disperse and your haters shall flee' (במדבר י:יד) Is there truly anyone who hates the Creator of the world? This comes to teach that anyone who hates Israel is as if he hates Hashem." Also see (ספרי מטות קנז): "You are not avenging the vengeance of human beings, rather the vengeance of Hashem."
Chazal further spell out the parameters of vengeance on the verse that teaches us the prohibition of vengeance against fellow Jews (תו"כ קדושים ד): "'You shall not take revenge or harbor resentment against your brothers' (ויקרא יט:יח) but you take revenge and harbor resentment against others.
There is a double standard. One for Jews and one for gentiles (I am sure chazal did not advocate random acts of vengeance against random gentiles. However, when an entire society sets up the Jewish people as its enemy, then that whole nation becomes the enemy of Hashem.)
Of course there is another side to this coin. regarding those who forgo their honor and forgo revenge it is said (Yoma 23a): "Those who are insulted and do not insult, who hear their disgrace and do not respond ... on them the verse says 'and those who love [Hashem] are like the coming of the sun in its strength.'" When the impetus for revenge is personal. When the Honor of Hashem is not what is at stake, then a person should overcome his personal, selfish desire for revenge.
Rav Kook Zt"l in his chidushim on shulchan aruch (O"H 1:1), distinguishes between a intrinsically good midah and a midah that is not intrinsically good but can be used at times for good purposes. The first kind is something we are interested in acquiring at the root of our being. The second, however, is a midah we do not want to integrate into our soul but rather keep outside and use when it is necessary. Vengeance of course, must fall into this second category. Personal revenge can cause tremendous evil in the world. It is only a society that is sensitive of the Honor of Heaven that can safely implement it without causing itself damage.
There is more, of course. (eg. Pinchas, Pesel Micha, Shimshon) I just wanted to demonstrate that revenge is not considered a universally evil concept in Judaism. On the contrary, it can be source of great Kidush Hashem when implemented against the wicked in the world. As David Hamelech writes in Tehilim (58:11): "the righteous man shall rejoice when he sees vengeance; he shall wash his feet in the blood of the wicked."