Can I reasonably move universities every few years for professional work? My real love is scientific computing, but I'm generally interested in nearly every academic field — through undergrad I've had research computing positions in social psychology, electrical engineering, volcanology, and pharmaceutical sciences. Now I've graduated, and I'm at a different university doing data analysis in cognitive science. I like it, but I have a long list of places I'd like to live and fields I'd like to learn more about, and my "career plan" is to move every 3–4 years and work at a different university in a different field, always doing scientific computing/data science though. I'm not too concerned about getting a huge list of academic accolades or getting a PhD right now; I'd rather just be doing interesting work.

I've mentioned this to several professors and graduate students who have asked about my plans, and they always react as if I've said I want to run off and join the circus. Is there some truth to how they react? Am I hurting my career this way?

I'd like to clarify that I just want to be doing data analysis. It seems like nearly every lab needs people to do this, so I don't see how I'm a funding leech.
As a data scientist myself, I have found it rather difficult to be a journeyman data scientist in academia. Yes, people need their data analysed; no, they do not want to pay for your full salary, benefits, and office space. Nor are they necessarily going to hire an outsider to analyse their data. They can get their postdocs/grad students to do it. 

I have met repeated resistance to being taken onto projects as an outside data analyst. Certain STEM disciplines are especially bad with this. Because I have a PhD, I can find full time positions that allow me to be housed in a department, teach classes in that department, and then take on outside projects as I find them. These outside projects are never enough in and of themselves to provide enough work for me to retain my job. The fact that I can do independent research and teach classes is what allows me to do what I do. 

I just think being a journeyman data analyst in academia can be a rather tough life, and you may not have much freedom to actually decide what type of subjects you are exploring. In my experience, you may rank below even the master's students and will possibly be paid subsistence level pay.