How do you know for sure whether or not to use a closing? One good test is to ask yourself whether this email is more akin to an instant message/text or a business letter. If you're giving your teammate a quick update on an ongoing project, a formal closing might not be necessary; if you're throwing your hat in the ring for a promotion, it definitely is required. When all else fails, and you're still not sure, err on the side of caution and include it. You'll never go wrong by being too polite and respectful.
However, before using a general salutation (or leaving off a salutation), try to find out the name of the person you are contacting. If you are applying or inquiring about a job and the hiring manager’s name is not included on the job listing, you might look up the title of the employer or hiring manager on the company website. If there is a contact number, you might also call and ask an administrative assistant for the name of the hiring manager. If you are sending a different type of letter, you can still look up the person’s name on the company website, or speak to an administrative assistant or contact at the company for the name of the person you are trying to reach.