In proper American English (I'm not sure about other English-speaking countries), it is inappropriate when asking permission to say, "Can I open the door?" for example. Of course you can open the door. Unless you had no arms... The correct question to ask is "May I open the door?" Both are used in the spoken language, similar to the problematic ain't mentioned above. When it comes down to it, though, can I is wrong in this situation, at least so far as modern American linguists have to say about it.