fifteenth letter of the alphabet, from a character that in Phoenician was called  'ain (literally "eye") and represented "a very peculiar and to us unpronounceable guttural" [Century Dictionary]. The Greeks also lacked the sound, so when they adopted the Phoenician letters they arbitrarily changed O's value to a vowel. (Thus there is no grounds for the belief that the form of the letter represents the shape of the mouth in pronouncing it.) The Greeks later added a special character for "long" O (omega), and the original became "little o" (omicron).

In Middle English and later colloquial use, o or o' can be an abbreviation of on or of, and is still literary in some words (o'clock, Jack-o'-lantern, tam-o'-shanter, cat-o'-nine-tails, will-o'-the-wisp, etc.).

O' the common prefix in Irish surnames is from Irish ó, ua (Old Irish au, ui) "descendant." 

The "connective" -o- is the usual connecting vowel in compounds taken or formed from Greek, where it often is the vowel in the stem. "[I]t is affixed, not only to terms of Greek origin, but also to those derived from Latin (Latin compounds of which would have been formed with the L. connecting or reduced thematic vowel, -i), especially when compounds are wanted with a sense that Latin composition, even if possible, would not warrant, but which would be authorized by the principles of Greek composition." [OED]

As "zero" in Arabic numerals it is attested from c. 1600, from the similarity of shape. Similarly the O blood type (1926) was originally "zero," denoting the absence of A and B agglutinogens.

As a gauge of track in model railroads, by 1905. For o as an interjection of fear, surprise, joy, etc., see oh.

The use of the colloquial or slang -o suffix in wino, ammo, combo, kiddo, the names of the Marx Brothers, etc., "is widespread in English-speaking countries but nowhere more so than in Australia" [OED].

word-forming element meaning "like, like that of, thing like a ______," from Latinized form of Greek -oeidēs (three syllables), from eidos "form," related to idein "to see," eidenai "to know;" literally "to see," from PIE *weid-es-, from root *weid- "to see." The -o- is connective or a stem vowel from the previous element. Often implying an incomplete or imperfect resemblance to the thing indicated.

word-forming element indicating "branch of knowledge, science," now the usual form of -logy. Originally used c. 1800 in nonce formations (commonsensology, etc.), it gained legitimacy by influence of the proper formation in geology, mythology, etc., where the -o- is a stem vowel in the previous element.

The second element is prop[erly] -logy (-logue, etc.), the -o- belonging to the preceding element; but the accent makes the apparent element in E[nglish] to be -ology, which is hence often used as an independent word. [Century Dictionary] 

word-forming element, from Greek -oma, with -o-, lengthened stem vowel + -ma, suffix forming neuter nouns and nouns that indicate result of verbal action (equivalent of Latin -men); especially taken in medical use as "morbid growth, tumor," based on sarcoma, carcinoma.