Really good question. I see lots of internship related questions on CareerVillage and it's really great to see that young people are inquisitive regarding them. I would say that internships are not required, but I HIGHLY HIGHLY recommend doing at least one (if not more). When you apply for a full time job after your graduate college, many job employers will ask about your work experience and skill set. Internships prove that you are not only capable and hard working, but also that you likely developed a new skill through this experience. Internships show an employer that you are willing to go above and beyond what is required and these are the types of things that employers like to see. You will only be a more marketable and stronger candidate with a few internships "under your belt" compared to someone who has done no internships. When you graduate, you will be competing with many other recent graduates for a finite amount of entry level jobs. The competition is fierce and one way other than your GPA to "rack and stack" applicants is via their work history. Applicants with internships on their resume are seen as more desirable and competitive and likely have more to say during an interview. During interviews you will be asked "Tell me about a time where..." "How would you handle X based off of your past experiences" and other behavioral questions which are used to judge how you think and how you operate on the fly. These questions are easy for people who have internship experience, not so much for those with no experience.
That withstanding, it is important to find an internship that relates to something you like, your major, or your career goals. Having an internship just for the purpose of being able to put something down on your resume I do not recommend. There are tons of internships out there for nearly everything and you should be able to find something that is relevant.
In short, I highly recommend that you find relevant internships as they will only make you more competitive for when you apply for a full time job.
I hope this helps and I wish you the best of luck!!