Is it possible to work full time and complete a PhD?

I am doing that right now. I have a full time job and am working on a PhD in Computer Science. It is definitely possible, but has been the hardest experience of my life. I am past the hardest part and am wrapping up my first publication. I've also been at it for 3 years (already had my masters degree), so it's taken me much longer to get to this point than it would be for a full time student.

It has been extremely stressful and you can kiss your life outside of work+school goodbye. You will also need to be very good with time management and be aware that over the course of several years, there will be life events that pull you away from school.

When I was deciding whether or not to do it, I vastly underestimated the amount of time and energy required. I'm very glad I stuck with it so far, but I have to say, if I had an accurate picture of the workload I probably would have opted against it.

You need a huge amount of dedication to the goal in order to pull this off. If you have only a casual interest in the degree, then you will probably fail. I think I remember somewhere that the graduation rate for PhD's is around 50/50. Add a full time job on that and the odds are against you. But it is absolutely possible to overcome that with enough effort.

Each situation is different, and it might be hard to generalise, but roughly speaking, you can see a PhD thesis as requiring about 3-4 years working full time. For some people it might be a bit less, for others a bit more, but that's a good average. In addition, a PhD includes of course "technical" work, but also "academic training", such as learning how to write a paper/thesis, presenting papers at conferences, supervising students, etc.

Now, two cases are possible: either you already have some technical material from past work (e.g., you've been working 20 years in industry), in which case you have already completed some of the 3-4 years, and you mostly need to focus on how to output your work; or you don't, in which case, you still need to complete all of the work.

I've known some people in the first case, and they managed to do a PhD while working full-time. They would usually come in half a day per week (in agreement with their company), and work at home in the evening. In the second case, it seems unrealistic to do both a full time job and a full time PhD. In some fields, you might be able to do a PhD over 7, 8 or even more years (I've heard about someone in history who wrote his PhD in 7 years, while working full time as a school teacher in the mean time), but it might not be the case everywhere.

In addition to Daniel's answer, and including Sylvain's comment, I'd add that some French universities forbid starting a PhD without having some source of income, either through some funding or through a full-time job. Most funding forbid to have a full time job on the side, and if your full-time job is completely unrelated to your PhD topic, then you might have the green light from the administration, but not from the academic institution in charge of the PhD programs.

EDIT: I somehow forgot to mention that the indicated amount time in my answer concerns good PhD, and by good, I mean a PhD that will allow you to get a job in academia afterwards, which mean not only getting the degree, but also getting good publications, good collaborations, good reference letters, etc. If you only care about the title, then you might find some universities happy to make you pay tuition fees to deliver you a diploma after a few years. If you want to go to academia later, then you need to be a junior researcher for a few years, in order to demonstrate that you might be worth hiring as a confirmed researched, and then later as a senior researcher.

Virtually Impossible.

Doing a PhD is a full-time job that requires vast amounts of commitment in terms of mental effort and time. If the PhD research comes in number two position, then the results will never be very good. Also, not being available in the department to interact with your colleagues and supervisor will severely reduce the benefits you gain from the experience. Even if you finished the PhD, it may not be really worth anything, because you won't have been able to fully commit to doing it well.

On the other hand, you may have staggering genius and be ridiculously productive and have a fountain of energy, and then it should be doable.