It surprises me how many people get this wrong, even educated people. Since grammar is the number one more important thing in this whole world to me, I felt the need to make this post. This is my effort to make the world a better place.
If you are referring to yourself in conjunction with another person, whether you refer to yourself as "I" or "me" depends on whether you are part of the subject or the object. Here is the correct way to do it:
subject: Bob and I are going fishing.object: Everybody cheered for Bob and me.
If you are ever in doubt, just eliminate Bob, leaving yourself, and it will become very obvious.
subject: I went fishing.It really is that simple.object: Everybody cheered for me.