I think this one somehow takes hold when we’re kids. A child says, “Billy and me want to go out.” He’s immediately told to say, “Billy and I.” That takes hold, and he says “Billy and I” all the time, whether it’s appropriate or not.

This one is simple. When using I or me with a name or another pronoun, ignore the other name or pronoun! Choose I or me as you would normally if it were standing alone.

• Billy and I/me want to play.

becomes

• Billy and I/me want to play.

Obviously, “I” is the correct choice.

• Give the toys to Billy and I/me.

becomes

• Give the toys to Billy and I/me.

This time, “me” is correct. You’d never say, “Give the toys to I.”