Is it possible to attend my "backup" school but reapply to my top choice and go there if accepted? I applied to several graduate programs and was accepted to my back-up choice. The professor at one of my top choice schools contacted me personally to say that he was interested in my application but had no room for me this year; he suggested applying next year, as "re-applicants" have a good chance of getting accepted on their second attempt.

Though pleased, I mentally dismissed this. I had a tangible acceptance to a school I did want to attend (albeit last choice), and I enrolled in classes. I immersed myself in my new environment, took on a healthy course load with a teaching assistantship, and have received lots of praise for my work and work ethic from my professors and colleagues.

However, with each week I am here, I hear more and more people--students, professors, the head of the department--admit that my program is lacking in many ways. The school offers very few courses in my actual field (a fact they omitted on the school website that boasted what the program had to offer its students). There are two professors in my field, and one is always away. One of them has also been known to cancel classes frequently, a fact that had been addressed to and dismissed by the department. This means that the few opportunities I have to study in my field have decreased. The program is very heavily based on teaching--that is, the teaching as part of my assistantship. Two of the required classes I am taking this semester are teaching-oriented, and while I am happy to teach now, it is not a long-term career goal of mine, and I expressed this to my advisor. It seems, though, that despite what I was made to understand before coming to school, that this program ultimately tailors its candidates for a teaching career.

Ordinarily I would just accept it, as each program has its problems. Yet, I cannot shake the fact that, especially given the last fact, I am going to be geared toward a career I specifically do not want. Add to that the invitation from the professor of one of my top-choice schools, and I find myself wondering if it is unprecedented for a graduate student to switch. I would not be losing any time; if anything, a switch would save time, as the program I am currently in is unusually long, whereas the program I would be entering is comparatively shorter and more compact. Plus, as the assistantship the other school offers is not a teaching-based one, I will be able to take courses in the field of my choice. But before I keep considering, I would like to know if it is even possible.
Common scenario: a professor is recruited to go work at a different university; s/he takes his or her students along.  No one bats an eyelash.

The quicker you can make the change the better; you need not feel at all guilty.  It's just not a good fit.  Your current school would be a great fit for someone who wants to teach.  But it's not a good fit for you.