Could've, Should've, Would'veHow to use contractions with "have" correctly
The auxiliary verbs could, should, and would should never be followed by the preposition of. This error is a misinterpretation of the contracted forms could’ve (“could have”), should’ve (“should have”), and would’ve (“would have”); the contracted have sounds a lot like of when spoken. (Although contractions like these are generally not used in formal writing, they are accepted forms.)
I should of remembered not to use of after should on my essay.
I should’ve remembered not to use of after should on my essay.
I would’ve gotten a better grade if I had remembered.
Common Errors in English Usage: Errors in diction and idiom commonly made by native speakers of English
List of Common Errors in English Usage (PDF): Printable version of the complete list
Common Grammar Errors: A list of common errors in grammar (topics like subject-verb agreement and parallelism) as distinct from usage