I agree that a polite declination is all that is ever needed in most situations, especially if a reason is financial ("Mr. Adams regrets that he is unable to accept your kind invitation to . . .").  But I recall Miss Conduct giving somewhat contrary advice in an on-line chat a few months ago.  Providing a specific reason only invites debate.  If one has a nonrepeatable conflict, such as "Oh how coincidental, I'm getting married ont he same day!" then perhaps the reason could be shared.

My brother in law had a destination wedding in the British Virgin Islands nearly 20 years ago.  We had two young children and it wasn't practical for the whole family to go so my wife went to her brother's wedding and I stayed home with the kids.  The only people from either family who attended were the parents and the siblings of the happy couple and we assumed that that was how they wanted it.  When my wife accepted and I declined the invitation no questions were asked and no discussion ensued.

If the acoustics are good and I feel like whistling I'm going to whistle and I hope it doesn't bother you but if it does, sorry, I'm going to whistle anyway.  If the boss tells me to knock it off, that's one thing, you telling me to knock it off, that's another thing.