Well, one of the ways I care for my clothing is by properly hanging them in my closet. If I could, I would probably hang every piece of clothing I own since the benefits are numerous. Hanging minimizes wrinkling, airs out fabrics, and helps retain the overall shape of each garment. Unfortunately, I don't have a gigantic walk-in closet in my apartment, so I have to pick and choose what I will hang, and what I will fold.
Here is how I personally do it:
Collared shirts (dress shirts, OCBDs, etc.): Wrinkled dress shirts are no good- they are a must-hang. Wrinkled casual collared shirts are not as bad, but I still like to hang them up.
Dress pants: I generally use a regular triangle hanger and pass the pants through, letting them lay half on one side, and half on the other. You could go a step further and get a pant hanger as well. This reduces wrinkling, and properly airs out the pant.
Suits: Don't ever fold a suit, unless you're packing it for travel. Make sure both the pants and the suit are hung, and preferably on a hanger that has wide shoulders. Using a wire hanger could ruin the shape of the suit, and you wouldn't want that.
Sport Coats / Blazers: Just like a suit, make sure to hang sport coats on wide shouldered hangers.
Jackets: Rain jackets, parkas, field jackets, you name it. I hang them all so that they can dry properly, and also to be easily accessible.
Outerwear: My coats all get hung for the same reason as my jackets. Plus, I bet outerwear takes up more space when folded than they do when hung anyway.
Belts: The way to properly hang a belt is by letting them lay straight down. You can do this by hanging your belt buckle up on some sort of clip or belt hanger.
Ties: You can roll ties up and store them, or hang them on a tie hanger. I prefer hanging them.
Knits / Sweaters: Sometimes hanging a sweater might seem like a good idea, but I've had sweaters stretch weirdly as a result. Thus, I fold.
Fleece: My NorthFace, Columbia, and Patagonia fleeces all get folded, but I can see why you would want to hang them too.
T-shirts / Long Sleeves: T shirts, henleys, and other thin shirts really don't have much shape anyway. I prefer to fold them.
Polo shirts: I've seen polos get weird in shape from hanging as well. I fold these, as seen above.
Casual pants: Cords, chinos, cargos, and other casual pants all get folded. Generally hot dog style, then in half, thirds, or quarters.
Jeans: I fold most my jeans, but sometimes like to hang my raw denim. Unlike washed denim, raw denim requires a bit more airing and are prone to creases.
Shorts: Shorts don't take up much room, just fold them once hot dog style, and you should be good.
Socks: Does anyone hang their socks?
Underwear: More importantly, does anyone hang their underwear?
So there you have it. My hanging and folding habits.
Just FYI, I personally hang most my clothing on thick wooden hangers. Why? First, because they make my closet aesthetically pleasing to look at each morning, and second, because they help preserve the shape of my clothing a lot better than thin plastic hangers or worse, wire hangers.
Yes, wooden hangers will cost you more, but I'll tell ya... they were worth every penny. Do yourself a favor and invest in some wooden hangers if you can, I highly recommend them.