I read NCL's policy of smoking/no smoking and see that one can smoke in their room. As a non-smoker, I wonder if the smell ever travels from one room to another. Also, if I end up in a room after the previous occupant was a smoker, will I notice any after-smell? Or do they clean the rooms that well? Thanks

They do clean the cabins very well and can eliminate most of the odors.

Whether you will smell any smoke afterwards depends upon how good your sense of smell is.

I've found that cruise ships tend to do a better job of cleaning out cigarette odors than hotels do. Of course, if your cabin happens to be an exception, just bring it to the attention of the cabin stewards and they will do their best to eliminate any remaining odors.