It is acceptable to break off a relationship with someone using a letter if you aren't comfortable breaking up with that person face-to-face. While it's not ideal, writing a letter can help bring closure to your relationship.
Ideally, when ending a relationship, a face-to-face talk is the way to go. However, it's not always possible or practical to break up in this way. If that is the case, a letter may be a suitable alternative. A break-up letter should be as clear and respectful as is possible. Emotions are probably running high, and it's important to maintain a level of respect for your partner and for yourself. Chances are, there are some lingering feelings between yourself and the person you are breaking up with, and those feelings should be handled in a sensitive manner.
Using a letter to break up may be appropriate if you are in a long distance relationship or if the reason your are breaking up may cause a hostile situation. Websites such as LoveToKnow.com provide sample break-up letter to use as a template. Once you have drafted a letter and delivered it to your partner, it is natural that they may have questions or want to discuss it further. Therefore, keep in mind that writing a break-up letter does not automatically disentangle you from the other person.