When your social calendar is full its impossible to attend every event to which you've invited. Inevitably, you'll have to turn someone down. Writing a regrets reply is a seldom followed form of etiquette; many people ignore the RSVP regardless of whether they intend to attend or not. A regrets reply doesn't have to be long; a few simple sentences apologising for your absence is sufficient. Politely send your regrets well in advance Your declining will likely make room for someone else to attend.
Follow instructions. If the invitation asks for a RSVP by a certain date, send your regrets reply by or before the appointed deadline. Realise that people ask for RSVPs for a reason; they need to know exactly how many preparations they'll need for the number of guests. Don't procrastinate because you're worried about upsetting someone by not attending. Show respect by informing them quickly of your planned absence.
Put it on pretty paper. Even if you simply check the "Regrets" box on the invitation, take the time to pick out beautiful stationery and send a handwritten decline note in a small card. Express your pleasure at being invited, and politely explain why you cannot attend. Wish them the best.
Keep it short. Your regrets reply shouldn't be a sweeping saga of your angst over not being able to attend. A few sentences of simple explanation will do. For example, "Mike and I are torn up over the fact that we can't attend Annie's wedding. Unfortunately, Margaret graduates from Harvard that same weekend, and we'll be out of town. We wish we could be there to kiss the beautiful bride."
Pick up the phone if the relationship with the person inviting you to her event is close. Wish her well and give your regrets in person. Don't allow the written formality to put distance between the two of you. If you make the phone call, still respond to the written RSVP with the "Regrets" box marked. Don't throw the count off for the official yes/no tally.
Send it with a gift. You many not be able to attend the event, but you can send a token of your affection and good intentions. Send the gift at the same time as the regrets reply to help soften the blow of your absence.