This might be the case where I'm posting something the entire world already knows, but during a casual perusal of Jezebel comments I learned a new grammar rule. Or, well, a grammar rule that's new to ME.
Maybe I can use the excuse a previous commenter brought up and just say I'm from North Carolina? Does that help at all?
Yep, that's the way you judge which one to use: if you remove the other person, what are you left with? So "and me" would be the correct usage here. But if it was "Anne and I went to the store" it's correct to use "and I" and not "and me" because you wouldn't say "me went to the store."
(This comment is referring to a tweet from Martha Stewart: "Here's a better shot of the beautiful and talented Anne Hathaway and I on the Today Show.")
The more you know :)