These are okay: 1) Would you mind if I smoke here= simple future tense question using present tense of smoke. Very polite and certain as in "I am going to smoke, if not here then I will over there. However, I really care about how you feel and respect it." 2) Would you mind if I smoked here= simple future tense question using conditional tense form of smoke. Very polite but less certain as in "I am probably going to smoke here but if you don't like it I may not do it." 3) Do you mind if I smoke here= Simple present tense (mind) question using present tense (smoke). Polite (because you took the time to ask), but it is more certain than it is polite. Therefore, it is not the most polite option. It translates a little like "I'm probably going to smoke here regardless of how you feel, but I may move away from you a little because I respect your space." Not okay: 4) Do you mind if I smoked here= simple present tense (mind) question using past tense for smoke. In the simple present, you cannot use either the past or future tense for verbs that follow the word mind. You must use the present tense. (i.e. Also not okay "Do you mind if I will smoke here") *** If you ask these questions in English, DO NOT worry too much about politeness. All three acceptable options are almost equally polite in a normal situation. Anyone listening will be grateful that you asked and will never feel insulted because you are not polite enough. The same is true if you substitute other verbs for "smoke" to ask permission for something.

1. Would you mind if: Is a polite request. Verb goes in past tense. 2. Do you mind if: Comes across more harshly. Verb goes in present tense. Hope it helped :)