I don't want to be labeled a prescriptivist but
Judy and myself watched the game.
is wrong.
Judy and myself is the subject of the sentence and the subject form of I is I. If in doubt, remove the other person(s) (Judy in this case) from the sentence: Would you say that "Myself watched the game" is correct?
![Wink [;)]](/emoticons/emotion-5.gif)
However, in colloquial speech, you can often hear "Judy and me watched the game". I
myself use it frequently.