This is rather broad, but generally forgiveness is recommended as healthy and meritorious -- but not always required.
It is a strongly meritorious practice at the beginning of Yom Kippur to state:
I hereby forgive anyone who has wronged me, with the following two exceptions:
- Someone who plans to continue to wrong me and receive forgiveness.
- Any money to which I still have a legal claim.
If someone smashed my car, I am fully entitled and expected to take him to court to receive compensation. (Note that civil cases between two Jews should generally be handled by a beit din panel of three rabbis; the litgants sign a binding arbitration agreement to use the beit din, which the state will then enforce. If one side refuses to use any beit din, the rabbis will authorize the other side to go to court.)
In theory, Leviticus 19:17 actually commands someone to admonish their fellow over a problem, rather than let resentment simmer; however this is only in a situation where discussing it is likely to improve the situation. There are a lot of nuances to this, please don't use this as a license to scream at someone or "admonish" them using a baseball bat.
Otherwise, when there's no other productive action left to take (e.g. somehow I know he smashed my car on purpose, but I took him to [rabbinic] court and he lied through his teeth and got out of it), then it's helpful to accept that G-d has plans to work things out, and walking around full of rage all the time isn't healthy. The Talmud talks about the personal strength of those who can hear a personal insult without immediately responding in kind.
We do not, however, have the same obligation-to-forgive found in some other faiths. Rabbi Abraham Twerski, who is a psychiatrist, was working with a patient (of another faith) who had been abused in her past, and was compounding her current condition by self-flagellating over her difficulty with forgiving her abusers. As a rabbi, Twerski wanted to tell her "but you're not obligated to forgive them!", but as a professional psychiatrist, he was expected to work with the totality of his patient, including her faith.