Both could be used. We tend to use 'Do you still....' to ask if the person is still doing something that they had done before in the past. However, 'Are you still...' conveys basically the same meaning. However, in the situation where the person is currently playing darts (in the last hour say) and you want to know if they have stopped or not just for that day or for a short period, you would say "Are you still playing darts?" In this case, the time frame is much smaller and much more recent.

Both are okay. However 'Are you still playing darts?' is a little ambiguous. 'Are you still playing darts' could mean, are you still playing right now (as we speak, when will you finish?) or it could mean do you still play darts these days? Sentence 2 'Do you still play darts' there is no ambiguity and can only mean 'do you still play darts (these days).

Rene, "Are you still playing darts?"can refer to something that is in ongoing, although you may not be doing it now.The present continuous can refer to something that is a hobby, habit, or present occupation as well as something that is going on at the present moment. For instance, the question "Are you reading Shakespeare?" can refer not only to the present moment but to any time in the recent past or in the near future. You may not be reading Shakespeare now but it is an activity that is ongoing. In the same way, "Are you still playing darts?" can be a question about your recent activity and not necessarily about the present moment. "Do you still play darts?" asks whether you play darts at all anymore. Perhaps you quit playing. The answer could be "No, I don't play anymore." or "Yes, I still play. In fact I'm playing in a tournament now (although you are not playing at the moment of the conversation.) Or the answer could be."Yes I still play darts. In fact I'm playing right now at the bar as I talk to you on my cell phone.Who told you I'm playing darts?"

Thanks a lot for all your support!!! :) It has been helping me to understand the difference beetween these sentences!