What is the best way to respond to "You have an answer for everything", "You always have to be right", or "You always need to have the last word"?

There are basically two main possibilities:

1. They're unreasonable.
2. You're unreasonable.

If it's the first one, it doesn't really matter how you respond. The best policy is to avoid dealing with people like that as much as possible.

If it's the second one then you should work on trying to fix it. That's the best way to respond.