@Paola,
Mother gave the cookies to Janie.
Mother also gave the cookies to I??? ( I don't think so).
Just because a lot of people say it, doesn't make it right. "I" is a subjective pronoun, meaning that it should only be used as part of a subject, never as part of the object.
Conversely, there is nothing inherently wrong with using the word "Me", as so many people seem to think. "Me" is an objective pronoun, meaning that it should only be used as part of the object of a sentence, never as part of the subject. But, as the object of the sentence, it the only first person pronoun that is correct to use. In fact, to replace the word "Me" with the word "I" as the object of a sentence is simply wrong, no matter how many people do it. I suppose that, like most bastardizations of the language, it will eventually come to be accepted with continued misuse, but currently it is still deprecated by nearly all authorities on the English language.