I'll assume that you have a good relationship to your PhD advisor and that you can have a reasonable discussion with him. If this is not the case, then ignore the following as you will potentially have much bigger things to worry about.
It sounds as if the papers have not been written yet, so I'd suggest you discuss this with him as soon as possible. Lay out to him which papers you want to write, what will be in them, and where you plan to submit them, and ask him if he would like to be a co-author on any of them.
Now, the important thing is that this co-authorship you're offering is not a free ride. I would assume that a good supervisor knows that this will imply a significant contribution to the preparation of the manuscript and/or any follow-up work that still needs to be done. If he is willing to actively contribute to the papers, then you have a bona fide co-author and nothing to worry about.
If your supervisor is not willing to contribute anything to your publications, then there is no reason to add him as a co-author.
In any case, you should be open and honest about your intentions. Your supervisor is a very important person in the critical post-PhD phase of your academic career, and even if you leave academia, he is your previous employer. In any case, he will be writing all your letters of recommendation, so don't do anything that may have a negative influence on your relationship.
In summary: Ask him first, and if necessary, remind him that co-authorship implies active collaboration. If he does actively collaborate, you have a good and valuable co-author, and if he does not, he will either not want co-authorship, or you will have a valid reason not to add him.
