רבונו של עולם
הריני מוחל לכל בן אדם
מי שהכעיס והקניט אותי
או שחטא כנגדי
בין בגופי בין בממוני
בין בכל אשר לי
בין אונס בין רצון
בין בשוגג בין במזיד
בין בדבור בין במעשה
בין במחשבה בין בהרהור
בין בגלגול זה בין בגלגול אחר
ולא יענש שום אדם בסברתי
Master of the Universe!
I hereby forgive anyone
who has angered or vexed me
or sinned against me
either physically or financially,
against my honor
or anything else that is mine,
whether accidentally or intentionally,
inadvertently or deliberately,
by speech or by deed,
in a plan or a fantasy,
in this incarnation or in another incarnation.
Let none be punished on my account. 
This prayer is found in the Habad Siddur, “Tehillat Ha-Shem,” compiled by Rabbi Shneur Zalman of Liadi.
Although I edited out the phrases “any Israelite” and “no man,” in favor of a more universal statement, this should be in every siddur. [note: I subsequently found alternative versions of this prayer in other siddurim, which use the phrase “l’chol ben adam” — any person — in place of “l’chol bar yisrael” — any Israelite. I inserted this into the opening phrase.]
The prayer is recited every night, except on Shabbat and Festivals, presumably to avoid introducing any unpleasant thoughts that might interfere with or distract from the special kavanah and joy at those times. I also can’t tell whether “Festivals” is meant to include “High Holidays.” But I would use this even then, if I felt that I needed to.
It’s prayed in the spirit of what the Talmud says:
“All who overlook what’s due them, their sins are overlooked.” 
“Whoever is compassionate toward others [and forgives wrongs done to him/her], compassion is shown to him/her from Heaven…” 
“In the course of the day that is now behind us, we may have been offended by other people. But we do not want to go to bed with a grudge in our heart against anybody. We want to go to bed with a peaceful mind, and with love in our heart for all of G-d’s creatures. So, we declare that we forgive everybody. It helps us enjoy a restful sleep, and it will also bring us G-d’s forgiveness. For G-d’s reward is in kind [with our own thoughts, words and actions].” 
This teaching — that our own sins are forgiven if we forgive sins committed against us — is certainly echoed in Christianity —
“…forgive us our debts
as we forgive our debtors
[or: those who have trespassed against us.]” 
and in Islam —
“The recompense for an injury is an injury equal thereto (in degree): but if a person forgives and makes reconciliation, his reward [i.e. forgiveness of his own sins] is due from Allah…” 
Certainly in many other places and sources, too.
The mention of reincarnation/”another incarnation” (גלגול אחר) is not typical of Orthodoxy as we ordinarily meet it; certainly not of Conservative or Reform Judaism. It’s far more common in Hasidut and Kabbalah (and those branches of Orthodoxy for which Kabbalah forms an integral element). Yet it changes nothing about forgiveness as an imperative. It only expands the field to be included in our consideration.
Forgiveness, then, is deeply rooted in Torah and should be an essential part of Jewish spiritual practice. That this element is shared with Christianity and Islam (and other traditions) can further validate it as a universal truth. It’s also something that should be a source of pride for us about Torah: While Christianity and Islam differ from our tradition regarding other details of observance and belief, they have held some essential teachings of the rabbis to be vital in their own traditions as well.
As Rabbi Shneur Zalman, the Alter Rebbe, teaches, we must practice forgiveness daily.
At night, as he specifies.
But perhaps even in the morning, at the start of our day, to prepare ourselves for the stresses we typically face.
For further discussion of this prayer, including comments by Rabbis from the Orthodox, Conservative and Reform movements, see:
 based on “Prayer before retiring at night” in Siddur Tehillat Ha-Shem (Habad); p. 118; I also incorporated one line from the ArtScroll Siddur “Ahavat Shalom,” p. 288: בין במחשבה בין בהרהור — …in a plan or a fantasy…
 Rosh HaShanah 17a
 Shabbat 151b
 Mindel, Rabbi Dr. Nissan; As for Me — My Prayer; Kehot Publication Society, © 1972; p. 301
 Matthew 6:12
 Qur’an; Surah 42:40 (“Shura,” or “Consultation;” translation of Abdullah Yusuf Ali; p. 1317-8). Even more explicitly:
“If one desires to be forgiven for his offenses he must learn to forgive others. Especially, if one seeks forgiveness from God, he should learn to forgive others for their offenses. If one desires that God overlook his weaknesses, he should learn to overlook weaknesses of others.” (M. Amir Ali, Ph.D.)
(Dr. Ali is the Managing Director of the Institute of Islamic Information & Education; Email: email@example.com )