A proper introduction in a letter depends on the purpose of the letter as well as on the recipient. For instance, a cover letter requires a much more formal introduction than an informal letter to a friend or family member.
A formal introduction for a letter of recommendation or cover letter for a job application sometimes eschews the "dear" salutation, but many people accept this greeting as a formality. However, many people do not recommend "To Whom It May Concern" because this does not address anyone specific. No matter the formal greeting, the introduction to the letter must begin with the important information, including the reason for the letter.
A formal letter such as a cover letter may also begin with information such as the reason for contacting the addressee. For instance, a letter of recommendation may explain that the writer intends to recommend a third party for a job position or other candidacy like a scholarship or academic position. Sometimes a writer begins the letter with a sentence to grab the attention of the reader while keeping an air of formality. Less formal letters have no hard and fast rules for formatting, especially since many people no longer write letters for personal reasons.