Usage Note: Generations of grammarians and teachers have insisted that can should be used only to express the capacity to do something, and that may must be used to express permission. But children do not use can to ask permission out of a desire to be stubbornly perverse. They have learned it as an idiomatic expression from adults: After you clean your room, you can go outside and play. As part of the spoken language, this use of can is perfectly acceptable. This is especially true for negative questions, such as Can't I have the car tonight? probably because using mayn't instead of can't sounds unnatural. Nevertheless, in more formal usage the distinction between can and may still has many adherents. Only 21 percent of the Usage Panel accepts can instead of may in the sentence Can I take another week to submit the application? The heightened formality of may sometimes highlights the speaker's role in giving permission. You may leave the room when you are finished implies that permission is given by the speaker. You can leave the room when you are finished implies that permission is part of a rule or policy rather than a decision on the speaker's part. For this reason, may sees considerable use in official announcements: Students may pick up the application forms tomorrow.
Source: The American Heritage