How applicable are software engineering internships to computer science research and graduate school? This fall I will begin my undergraduate degree in computer science at a top-5 program (to whom it offends, I'm sorry to use rankings). My goal after I graduate is to get a PhD so I can research and teach computer science. 

I understand it may seem fairly early to start thinking about the summer of 2016, but career fairs and application deadlines will arrive soon, and I'd like to prepare for internships and research opportunities as best as possible. Since my primary goal is to stay in academia (or non-industry research, if that's a thing), would an industry internship help me reach my goals? Is it worth the time to acquire a little bit of industry experience? To be a bit more clear, I have a massive list of opportunities I'd like to apply for next summer. Of the approximately 25 items on the list, 15 of them are software engineering internships. For example:


Google
Amazon
Facebook
Microsoft
NASA
Intel


Then, there are certain programs that I think I like slightly more, because it seems they are very research-oriented despite still being "industry":


Wolfram
Nvidia


The programs I am most interested in are purely research-oriented, and most are undergraduate positions at various laboratories across the country. Most of these are funded by the United States Department of Energy.

In Summary

I understand that research experience is very important to PhD admissions in the field of computer science. I'd love to gain as much research experience as I can, as long as I'm interested in it. Is it frowned upon to have little to no experience in industry, when applying to PhD programs? Also, before I get ahead of myself, I understand that it is quite difficult to get an internship position at any of these companies or laboratories.

Don't get me wrong, I love actually writing code and working on applied software projects. I just don't love writing code for a salary.
You are correct that research experience is extremely valuable for getting into graduate programs.  Internships are one way of gaining such experience, but far from the only way.  At a high-ranked university, however, there will also be lots of opportunities with professors, both during the term and in the summers, and those will be at least as applicable, if not more so, for getting into graduate school.  Industry experience as a full-time employee can be great for showing maturity and various skills not typically acquired during undergraduate, but frankly, you're not going to develop a significant and differentiating amount of such skills in a couple months as an intern either.

In short: no, you don't need industry experience to get into graduate school.