I'm seeing this phrase used more and more.
When I was at school, my teachers made a point of highlighting that this was lazy English, and that the correct phrase was "and I", but it all really depends on the context of the sentence.
"My friend and I went to a party last night" is correct.
"My friend and me went to a party last night" is wrong.
On the other hand:
"John invited my wife and me to the party" is correct.
"John invited my wife and I to the party" is wrong.
The basic rule that applies to this form of grammatical correctness is this:
I am the subject of the sentence, but the object of the sentence is me.