While a simple "Hi," "Hello," or even "Hey" is appropriate in casual correspondence, a more formal salutation is appropriate when you are emailing about a business_related matter, such as a cover letter, letter of recommendation, or inquiry letter.
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.