Your resume is arguable the single most important part of the application process. A well-organized, relevant resume will set you up to get an interview, while a poor resume will get completely lost in the sea of applicants. This is a fairly modern concern, as job postings now get thousands of online applications a day.
However, this is a case where you’ll want to use your common sense. If you went to college for marketing and had a marketing internship your senior year, then worked as a server for the next several years, you would want to include your marketing internship.