I know that a lot of people have trouble figuring out whether to use "I" or "me" when referring to one's self and someone else.
I am assuming we know it is considered correct (and polite or something) to put the other person first, but here is a trick to figure out if you should use ME or I.
We will employ the skills of the incredibly handsome and talented Jason Segel (who I might just have a GIANT crush on) and the fancy cookie maker, Martha Stewart, for this guide.
So we start out with our statement: "Martha and me want cookies!"
Then we take away Martha so we are all alone with Jason Segel (hubba hubba).
And we repeat the phrase again, without Martha this time.
Clearly, it is not correct, so it would be "Martha and I want cookies."
And it sounds just as weird when you reverse it.