I was in the exact situation of getting a verbal offer from a dream job in December and having 3 interviews in January. I went on all the interviews and would advise anybody else to do the same. There are some straightforward reasons why:
1) The offer you get is likely a verbal offer, not a written offer that includes all logistics. you don't 'have' the offer until your offer letter comes through. Usually it takes several weeks including back and forth negotiations to get the offer in writing. In the meantime, you should consider this job offer as promising but not definite. In addition, it is not until your offer comes through that you know exactly what resources are promised to you. (And as the poster above stated, you never know how those could change in the transition from conversations to a written offer).
2) How sure can you really be that it is your dream school? Perhaps it is likely that it will be, but you really never know. I was continually surprised in my interview experiences by how different my expectations and actual experiences were so I would not want to miss an opportunity to gain more information.
3) The nobility issue is a tricky one. It probably feels like the nobler thing to do is to cancel - to free up room for another candidate. However, on the other hand there is an argument to be made that the nobler thing to do is to stick with your commitment (especially if you don't yet have a written offer). If you cancel, you are communicating with them 'no matter how things go down with the offer from school X, I am already sure I do not want to work at your institution'. You could see how that might come off as somewhat presumptuous. I had an interview at a R2 school after my R1 (verbal) offer came through. I still went, and first off nobody seemed surprised that I didn't cancel, and second off nobody treated me as though I was wasting their slot. When asked I said that I couldn't pass up the opportunity to share my work and learn more about the university/department/research. This was true and I'm glad that I went because I was actually impressed… and if my verbal offer did not materialize as expected I would have been very thankful for having visited and allowing them to consider me.
4) There is also a selfish motive - that an interview is a chance to show your work and skills. To some extent canceling is a missed opportunity. (Obviously this motive should not dictate your choice but it is a consideration worth noting).
I know schools vary on this quite a bit, but I firmly believe that if a school wants you, they should wait for you to see the process through to completion. They understand how this works. You've gone on the market, you have received opportunities to interview at some portion of the places you have applied, and you need to see the process through. I did not receive any pushback on this (maybe I'm the minority on this - if so, I was lucky!). Also, you do not need to make any decisions (or even entertain making decisions) until you have the written offer letter in hand. If anyone tries to push you sooner, don't let them! How can you make a decision before knowing the terms of the offer?
In my situation, I did not receive the written offer until I was finished with my interviews. As soon as I got it and it was acceptable, I pulled out of the searches that were still going. I thought this was the right balance of not missing an opportunity to interview and learn about a department and doing the noble thing.
p.s. Someone else posted that it's weird how we as psychologists treat the job search (worrying about hurting others' feelings etc). I don't think it has anything to do with psychology. The academic job search in general is what's unusual. They have a semester-long job search, only at predefined times of the year, and then don't expect people to start working for another half year (or more, in the case of deferring!). Corporate jobs come and go all year round and hire on a rolling basis. And imagine trying to tell a corporate executive that you'd like to join their company but would like an extra year of training in a poorly paid job before starting :). I think this is all the more reason why candidates should let all of their opportunities play out. The university does not need you tomorrow, and all universities are on roughly the same cycle. It's the culture of the thing.
pps. I realize some schools do try to shortcut the cycle, I have not had any experience with that though. Based on everyone I've heard of in R1's, they had all the time they needed.