Bismillahi Rahmani Rahim
Salaam Alaikum wa Rahmatullah
I think the most lenient point of view is that three-dimensional images of anything that has a soul is forbidden. That would mean things drawn on a plane surface, like a picture or a painting, would be permitted.
The more strict ruling is that even flat images are haraam, except in the case of necessity, such as for ID cards. In textboooks in conservative countries such as Saudi Arabia, you will see pictures drawn in such a way that the head is separated from the body so it could not be construed as a "living" thing.
I personally do not know which of the rulings is more correct, but I tend to be conservative. I don't display photos of my family, though I will keep them put away in an album. I do cross stitch, but only of flowers or other plants or buildings. I have absolutely NO statues in my home. My children have action figures to play with but I don't like the little baby dolls that are so lifelike they look like real infants - those actually creep me out, lol. Most kids outfits have cartoon characters on them, and I don't worry about it, but I don't let my kids wear such clothes when they go to the masjid. I guess I come down somewhere in the middle. May Allah forgive me for any shortcomings in my understanding of this issue, Ameen.
Fi Aman Allah,
Nancy Umm Abdel Hamid