Just as bad: "Him and I", either as subject or object. "Him and I went to the store." "Susie came to the store with him and I."
I think of using "I" no matter what the circumstances as a kind of "me" phobia that people have when they haven't sorted out the subject/object thing, know that there's often an issue with using "me", and decide to err on the side sounding better by using "I". :)