Is "Can I have a cup of coffee?" polite? [closed]

To Sam's comment, the more pedantically-minded English speakers will state that beginning a question with Can I is to question one's own ability rather than to make a request. To satisfy those people, you're better off using may:

May I have a cup of coffee?

If you want to be polite about it, add a please:

May I have a cup of coffee, please?

If you want to be especially considerate, like when you need to get some coffee from a person who's had a bad day, make the hassle of getting the coffee the focus of the request instead of the coffee itself:

Could I trouble you for a cup of coffee?

Finally, if you're familiar with the person, you can just skip the question altogether without offense:

Pass the coffee, buddy.

It's common to assume a person who's looking for coffee is suffering from caffeine withdrawal, allowing for a good deal of leniency when considering how polite the request for coffee is.

Can has an abruptness to it that could come off sounding demanding.

Could I have a cup of coffee

or

could you help me find the beans.

would be better, and it never hurts to say please:

Could I have a cup of coffee, please? What do you mean this is a sporting goods store?