When writing a business letter, it's always good to use a standard business format, which typically includes the heading, the date, the opening, the body and the closing. It will make you seem professional to those you are contacting. Using "regards" or a variation thereof as a salutation is acceptable, even though it is considered slightly less formal.
To regard someone means that you respect that person and think highly of him, so when closing a letter, using a salutation such as "Regards" lets the person know that you are thinking about him. It is acceptable to use in both business and personal letters.
A variation of the salutation is by adding the word "kind" to it, and with this closing you are letting the person know that in addition to thinking about him, you are thinking about him in a favorable way. It's considered a polite way to end a letter.
Another variation on the salutation is "Best Regards," which is a way of communicating that you hold the person receiving the letter in very high esteem because you regard him in the best way, and is another way of politely ending a letter.
With Warm Regards
Some people like to use "With Warm Regards" at the end of the letter to add a more personal feel by using the word "warm." It's synonymous with "kind regards" or "best regards" as all of them are slight variations on the salutation. Most times, all of these salutations are an appropriate way to end a letter, and can be just as effective as a salutation such as "Sincerely."