“Rav” is great. The way Hebrew transliterates, it can also be “Reb” or “Rab.”
When any of these words are used as titles, they mean “Master.” Master of what? Learning. Specifically, Jewish law.
“Rabbi” is “my Rab.” “Rebbe” is another spelling, although it’s also true, as Jens noted, that when a Lubavitcher Jew say “The Rebbe,” he is speaking of Menachem Mendel Schneerson, of blessed memory.
“Rabbinu” is “our Rab.” You see “Moshe [Moses] Rabbinu” in a lot of Jewish commentary.
Ashkenazic Jews have used “Rabbi,” so that is what you usually hear in the US, though Chassidic and Chabad Jews usually use the “Rebbe” spelling, and pronounce it slightly differently.
Sephardic Jews tend to use “Rav.”
In the US, where most people don’t know the Hebrew origins of the word, Rabbis use “Rabbi” as a title, as in “Rabbi Samuel Friedman.”
In Israel, where people understand the possesive suffix of “rabbi,” using the word as a title sounds a little odd. People address rabbis the their faces as “Rabbi,” but when rabbis use a title in Israel, it’s usually just “Reb.” Or “Rav.” Transliterate how you want.
When a person is called to the Torah by his or her Hebrew name, and the person, or his father or mother is a rabbi, “HaRav,” “the Rab[bi]” is used. Examples: I am just plain “Rivkah bat Moshe u’Malke Rina,” (Rivkah, the daughter of Martin and Regina), but if my father were a rabbi, I’d be “Rivkah bat HaRav Moshe, u’Malke Rina.” When my cousin Eva Leah finishes rabbinical school, she’ll go from plain “Chava Leah bat Yosef v’Chana” to “HaRav Chava Leah bat Yosef v’Chana.”
More than you wanted to know.
–Rivkah bat Moshe u’Malke Rina, v’achiyanit Yosef v’Chana