One of the major roles of the noun or pronoun is the object of the preposition. When a noun or pronoun combines with a preposition, it forms a prepositional phrase, which primarily acts as either an adjective (the book on the table) or an adverb (He drove to my house). The noun or pronoun hooked to the sentence by the preposition is the object of the preposition.
When a personal pronoun serves as an object of a preposition, it must appear in the objective case. Using the subjective case is a common mistake, portrayed in the title of the Oops Me book: A Grammar Book for You and I, Oops Me.
See objective case for a discussion of the objective case of pronouns,
Here are some common mistakes, with the fixes shown parenthetically (the preposition and the object of the preposition are underlined):
just between you and I
(just between you and me)
He prepared the report for Jane and I.
(He prepared the report for Jane and me.)
Here's a present for you and he.
(Here's a present for you and him.)