Polite requests with "I" as the subject

Examples:

(a) May I (please) borrow your pen?
(b) Could I borrow your pen (please)?

May I and could I are used to request permission. They are equally polite.
Note in (b): In a polite request, could has a present or future meaning, not a past meaning.

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(c) Can I borrow your pen?

Can I is used  informally to request permission.
Can I is usually not considered as polite as May I or Could I.

Typical Responses:

Certainly. Yes, certainly.
Of course. Yes, of course.
Sure. (Informal)

Often the responses to a polite request consists of an action, a nod or shake of the head, or a simple "uh-huh."

Note: Might is also possible. Might I borrow your pen? Might I is quite formal and polite; it is used much less frequently than may I or could I.


Cheers!
Naeem