Is it possible transfer from a MS program into a PhD program within the same school? I recently enrolled in a 2-year MS in HCI program.  My BS was in Computer Science.  Now, looking at my career goals and opportunities, I am wondering if it would be possible at all to email my director and ask if I could get into the PhD program (at the same school). 

Would this be feasible at all?  Would I have to completely re-apply? Or can I do 1-year of the MS and transfer into the PhD program? Or is that something that is frowned upon?

Just to point out, I am asking about transferring from a MS to a PhD program WITHIN the same school, not switching schools. I figured that if I were to switch schools, that would be an application process from scratch.
This is usually kosher, but it can depend on the school and field. The department might want to see what you do over the first year or so, both academically and in terms of clicking with faculty and their research. The best thing for you to do now would be to find a faculty member whose research really interests you and try to find opportunities to work with them. If that doesn't work right off the bat, sign up for a class they teach and kick ass in it, then try again. Once you have this relationship, and assuming you're producing good work for them, it's rare that they wouldn't support you staying on, so long as they have the resources to fund you.

You, as a Masters student, are essentially a free trial for the school/department/professor. They get to see how you fit in the department and what you're capable of *plus* they don't have to pay for you. If you're a good fit, there shouldn't be a reason why they wouldn't want to keep you. However, they'll likely still ask you to apply (formalities).