Work experience is not a requirement. However, for most applicants, having some work experience better positions them to be competitive in the application process. This advantage can manifest itself in the form of more compelling, detailed, and salient recommendations, greater insight in the essays, etc.
Frankly speaking, one wold need to be fairly distinctive and exceptional in order to get accepted as a fresher with no work experience. It is possible, but definitely not the norm.
Internships could count as work experience. You will have to exercise your best judgment as to how to classify the internship (full-time or part-time; professional work or volunteerism). If you have doubts as to whether or not an internship should be mentioned, do not bother bringing it up. An internship just moving papers around and acting as a courier in an office might not be worth mentioning for someone with more substantive full-time experience. It might be salient for others with less experience, but should be considered carefully. The governing question should be: does mentioning the internship improve the strength of the overall application?