I saw this article from Forbes: Americans Rank A Google Internship Over A Harvard Degree and thought it was worth highlighting.
It’s important to do well in school, and having a high undergraduate GPA helps immensely if one decides to go on to graduate school, get a MBA, etc. But an internship or two on a resume helps dramatically in getting that first job – they count as experience, which means you can immediately apply for those jobs that ask for 1 – 3 years of experience. Internships also give you something to talk about during interviews – how you handled difficult situations, how you handle meetings, and all those personality-style questions.
IMO the biggest value of an internship is to understand the corporate environment: learn how to dress, how to interact with colleagues and superiors, and to be able to compare yourself talent-wise and see where you need improvement.