It depends on the audience. It may be especially important to get the tone right in this situation, because it's possible that your recipient is upset, and you need to mollify them.
For instance, in a business letter, you might start with something like "I apologise for the long delay", and continue with a respectful tone throughout (without being obsequious). In a letter to a friend, something more light and humorous could work, but if the friend is really upset, florid apologies might be called for.
It may be worthwhile to try to think of something original here, since using stock phrases may not improve your correspondent's mood.