I am currently a major in computers and information technology with a concentration in web development. I have the education but I don't have much work experience. Right now the only web development internship I can find is an unpaid one. I am aware that unpaid internships are not considered legitimate work experience for jobs but will it help me get a paid internship in the future? Or is just a waste of time?
Internships of any kind (paid or unpaid, full or part-time; even volunteer work) are absolutely considered legitimate work experience for jobs and for other internships. That's the whole point of the unpaid internship-- your compensation is in the form of work experience that you can use to give yourself a leg up when you apply for either jobs or paid internships.
An unpaid internship is by better than having done no work at all. At the very least, you will have references to vouch that you are a good employee.
The kind of work you do will determine whether future potential employers consider the internship "valid work experience." You'll want to be able to show them that the projects you worked on in the internship prepared you for the work you would do for them. If the internship consisted of coffee-fetching and typing, then it might be a waste of time you could be using to work on your portfolio.
See whoever told you that unpaid internships doesn't matter is completely mistaken. These days, many internships are unpaid but more than anything, it’s the experience that matters. Hiring Managers value a candidate having valuable experience. Yes, you should put your internship project work on your resume, as long as it’s relevant to the position in which you are applying. Here you need not to mention in your resume that these jobs were unpaid. So just include what you did and believe me nothing is mere waste.
I think an unpaid internship is a bad idea. If you can't find a paid internship in your country, maybe try abroad (if this is something that interests you)? I know in my home country the economy is failing, so people do get the sense that an unpaid internship with the potential for a job is better than nothing, but in the country I currently live in, nobody, and I mean, NOBODY, with a CS degree (or working towards it) would accept that and no self respecting company has the gall to offer it. The only way one would work for free is if they were doing their own startup as another poster pointed out.
Also, if you have the discipline, instead of working for free, you can use your time to contribute to open source or do personal projects or read programming books. Someone with a good github account or open source experience is a very attractive hire, if not in your home country, then where the action in CS is at.
Unpaid internships are a great way to show your work ethic to a company you actually want to work for and it's great for networking. You also get hands on experience, as an unpaid intern, few expect you to know everything about the technical aspects of a job. So, several people are willing to help you learn and establish your career. From my unpaid internship I wasn't looking for a paycheck, I was looking something that I could you to give me a step up in my career and what's in my bank account doesn't do that. It's the knowledge I learned from my internship, the connections I made with managers, who did help me get a well paying job and continue to invest in my success. For me that was more valuable than a paid internship.
"If you're dumb enough to work for free, you're too dumb to work here."
The point of course, is that nothing of value can be contributed by someone who doesn't value their own contribution.
I've watched a lot of grad students waste their time in unpaid internships. What is there to be gained by working for free? From a business standpoint, unpaid interns are risky because they have absolutely no stake in the game. Employers will more often than not keep you from where any of the real action is because you're an unpaid, unproven liability. Interns gain access to trade secrets, business strategies, and strategic conversations...yet offer very little in return that can be used by the company to grow itself and continue to make money.
You're getting a degree in one of the hottest industries on the planet; you would be wise to start your own business and start picking off the low hanging fruit that the larger companies are ignoring. You'll learn infinitely more by working from the ground up, and your resume will look 100x better than the shmucks' that spent summers making coffee for blue-chip bigwigs. In a worst case scenario, your business fails...but you made exactly the same amount as if you were working for free, and the experience will be recognized for its true value, giving you a huge edge over people competing for the same jobs.