Have vs. Of

Quite often, people are thrown by the way a phrase is pronounced, and they subsequently carry the confusion into their written text.  I often see incorrect usage of the word "of," as in the following examples: Should of / Would of / Could of / Must of.  There are no such expressions in American English.  In all cases, the second word should be have, not of.  The correct phrases are should have, would have, could have, and must have.

When these phrases are spoken, people will often use the contracted form of the two words, as in: Should've/Would've/Could've/Must've, which doubtless led to the mistaken belief that the second word is "of" rather than "have."  Sometimes in casual speech, folks will use the slang terms "shoulda," "woulda," "coulda" and even "musta," which helps to blur things further, especially given the fact that the slang word "kinda" does mean "kind of."  In informal writing, the proper and correct contractions for Should have/Would have/Could have/Must have are Should've/Would've/Could've/Must've.  In formal writing, it is best to spell out the two words.  In any case, the word "of" is never used.

The foregoing refers to phrases of intent.  For other usages, such as "I must have a cup of coffee now" or "The dog should have a bath," it would be incorrect to write or say "must've" or "should've."

To summarize:

Should of, would of, could of and must of are all incorrect.
The correct phrases are: Should have, would have, could have, and must have.

The contractions should've, would've, could've, and must've are used informally.

Incorrect: "We should of gone to the beach."  "I must of left my bathing suit at home."
Correct: "We should have gone to the beach.  "I must have left my bathing suit at home."  "We could've gone to the beach today."  "We would've gone to the beach if it hadn't rained."