Well, in normal dreams I can do just about anything. In lucid dreams, I’ve only done two things, however - flying and walking through a wall. The flying was easy - no problems there except I had a tendency to do it indoors and bump up against the ceiling. I don’t know what the limits were, if any, because I wasn’t interested in finding them. Walking through the wall took a couple of tries (I wouldn’t have tried at all except that the door was locked at the time), but all it took was persistence to get it to work.
I remember the latter particularly well, because it was something I’d done many times in normal dreams, but in the lucid dream it was very different. It felt like I was literally squeezing myself through something solid, and fairly cold. And I had to go in sideways. But I got there in the end. Actually, I think I prefer that way of going through walls as compared to the quick phase I normally do, because it feels more “realistic” somehow.
Oh yes, and I made a room spin around me while I was flying once, but I was feeling a little dizzy at the time, so that might be why. I hadn’t really been intending to make that happen, but I did.
Those are the only powers I’ve had in lucid dreams, but I’ve made up a list of all the ones I’ve had in normal dreams, too, and how often they occur. I won’t write them all here, but the list is in my dream journal if you’re interested.