That to me is just rude, especially if it is a formal invitation.

Just respond "No. I have other plans. Thank you for the invitation."

If they ask you in person, insisting you come, you can still be polite. The continued insistence after that means they are insecure about something. That is when you start getting into the snarky comments and risk losing an acquaintanceship.

Now Jim, it depends on what she means by "invitation." If you're being invited to participate....

I liked Oscar Wilde's approach:

“I must decline your invitation owing to a subsequent engagement.”

Ah. Don't miss the chance to use this gem from M*A*S*H: "I consider marriage the headstone of American civilization."

Another by Oscar Wilde: "One can always be kind to people about whom one cares nothing."

You got some funny advertising going on Amy. Right under the "Participate in a Roman Orgy" ad for some role-playing game is an ad for "How to get pregnant fast at ConcieveEasy"!

From "Play It Again, Sam," by world-famous playwright who writes only about himself, Woody Allen.

What are you doing Saturday night?

Committing suicide.

What about Friday night?

Also Woody Allen:

I couldn't make it last week. My raccoon had hepatitus.

Um, thanks -- I write manners books! I guess I need to spell it out: I'm joking. I said "tempting." Of course, I'm not going to respond that way for real to an invitation. (It's nasty to hurt people's feelings when it's possible to lie one's way out of that. Honesty is often anything but the best policy.) -- Amy Alkon at July 31, 2012 11:50 PM

Amy,

Trust me, I know. I have learned some small chunks of social knowledge from you over the years. (Hint: Click on the Rude in my comment. ;-) I'm sorry I didn't catch the sarcasm of the post.