Modals are commonly used for asking permission Click for Audio
Can I ask you a question?
May I have a piece of cake?
Could I get you to turn off the lights
Some other common phrases are
Do you mind if I smoke?
Would you mind if I asked you something?
Is it okay if I sit here?
Would it be all right if I borrowed your lawn mower?
See also :
Grammar : Common Modal Usage
Textbook Recommendation : Touchy Situations, Chapter 7