List<Bitmap> avatars = new List<Bitmap>();

private void GameForm_Load(object sender, EventArgs e)
{
  avatars.Add(Properties.Resources.Head1);
  avatars.Add(Properties.Resources.Head2);
  avatars.Add(Properties.Resources.Head3);
  avatars.Add(Properties.Resources.Head4);
}

private void pictureBoxAvatar1_Click(object sender, EventArgs e)
{

  if(pictureBoxAvatar1.Image == avatars.ElementAt(0))
  {
    pictureBoxAvatar1.Image = avatars.ElementAt(1);
  }
  //I have four total possibilities, but just have this one statement until I figure it out

}

private void pictureBoxAvatar1_Click(object sender, EventArgs e)
{
   pictureBoxAvatar1.ImagePointer = (pictureBoxAvatar1.ImagePointer + 1) % avatars.size();
}

int avIndex = avatars.IndexOf(picturebox1.image);
avIndex++;
if (avIndex >= avatars.Count)
{
  avIndex = 0;
}
picturebox1.image = avatars[avIndex];