Our family room used to be 2 rooms -- a nursery / playroom, and a study / mudroom with BIR. But both rooms were small and didn't get used for playing or studying as the kids would just follow us around and then we'd all trip over each other. So we knocked down the wall, which unfortunately meant losing the BIR.
Our new family room has a sofa, a craft table (for kids' pasting, painting etc...), a desk (for my computer and paperwork), a dining nook (stores board games and puzzles and such, and will eventually be used for homework), some bookshelves (for books and toys) and lots of floor space, which is essential as I have 3 boys who like to wrestle and drive cars around and stuff.
Our living room is our library, media room, and entertaining space. I have a big chest coffee table that stores a LOT of stuff, and there are boxes with some puzzles and things, but in general, it's a quiet, grown-up space where we all get together to read, listen to music, or just chat. It's a pretty small room, and took a while for me to turn it into a workable space.
Our guestroom gets used often as all our relatives live out of state or overseas, so when they come to stay, they're here for weeks at a time. My children use it for napping, and DH and I put the baby down in there so that he's near us until we go upstairs to bed at the end of the night. It's an odd-shaped room as there used to be a fireplace on an angle in the corner, one side is taken up with a window, another side has the door, and a 3rd side is a very shallow space before you hit the doorway and fireplace corner. So it's really hard to fit any furniture in here without making it horribly cramped and claustrophobic.
We did look at converting our front porch into a sunroom / mudroom, but the cost knocked that idea on the head.