Rav (Heb. רב) is the Hebrew word for rabbi. For a more nuanced discussion see semicha. The term is also frequently used by Orthodox Jews to refer to one's own rabbi.
In the Talmud, the title Rav generally precedes the names of Babylonian Amoraim, whereas the title Rabbi generally precedes the names of ordained scholars in Palestine (whether Tannaim or Amoraim).
In the Talmud, Rav or Rab (used alone) is a common name for Abba Arika, the first Amora, who established the great yeshiva at Sura, which, using the Mishnah as text, led to the compilation of the Talmud.
In some Hasidic groups, the Rebbe is also referred to as a Rav; in other circles, the Rav is distinct from the Rebbe and is the highest Dayan (judge of a Jewish religious court of law) of the group.
The term rav is also a generic term for a teacher or a personal spiritual guide. For example, Pirkei Avot tells us that "Joshua ben Perachyah said: Provide for yourself a teacher (rav)."
The Rav
Nachmanides will sometimes refer to Maimonides as HaRav, "The Rav".
From the 16th century and onwards, Rav or the Rav generally referred to Rabbi Obadiah ben Abraham, a.k.a. haRav miBartenura (the Rav from Bartenura). Rabbi Obadiah miBartenura becomes an acronym in Hebrew for Rabbi `Obadiah of Bartenura (רע"ב).
More recently, as a sign of great respect, some rabbis are simply called the Rav even outside of their personal followings. Note that when the word is pronounced using a Patakh, the meaning is almost universally Rabbi Obadiah ben Abraham of Bartenura. When using a Kamatz, the term can refer to, among others:
See also the list of people called Rabbi.