Pick your battles. Why is it so important to tell this person that they are arrogant? What do you hope to accomplish? Most people don't enjoy hearing negative criticisms, especially when they are true.

Keep your cool. It's the best way to say something unpleasant, especially to the over-confident. It's much harder to argue with level-headed reason, though they will surely try.

Tell them like it is, but add some sugar. The arrogant are usually the most insecure people out there, which is why they put up such a big front. Say something like, "You're really confident and gutsy, which is something that I love about you. But I think you might be overdoing it. You're coming off as really arrogant, and it bugs me."

Move on. Leave before the storm hits, or simply change the subject and try to move on to more pleasant topics. Be sure to throw in a compliment or two to stroke the wounded ego of your arrogant friend/loved one.

Keep it light. Humor might be a good way to smooth over the situation and keep them in check in the future. "Uh-oh, your big old head seems to be floating away," and other such comments might help them to keep things in perspective, and might help you to coexist with them.