The best fall scarves are those made of cashmere. You want to buy either 100% cashmere, or a blend of at least 74% cashmere and 25% silk. Fall winds can be nippy, so you want something that will actually keep you warm, and nothing insulates you like cashmere. There are wool scarves that suffice, but they tend to be itchy and scratchy. Whenever you can, go with cashmere. Cotton won't keep you warm, but it's better than wearing no scarf at all when those winds kick up, or the air turns cold.
Denis Colomb makes the most beautiful scarves you'll find, and are carried at Barneys, Bergdorfs, Harvey Nichols and more. All scarves are hand-woven in Nepal, made of the finest cashmere. They are expensive, but if you're going to buy one good scarf as addition to your wardrobe that's also incredibly useful, it's worth the money. A scarf can transform your wardrobe, buying a great one, makes you instantly chic. This is the scarf worn by the stars in all the pictures you see throughout the year. So consider a scarf purchase as you would a great pair of shoes. A good one lasts years, a cheap one lasts less than a season.
Hermes makes gorgeous scarves, and are pricy but worth it. A great Hermes scarf makes a great entrance into any room. Chanel is also a beautiful addition to any outfit, you'll be instantly chic.
For the super indulgent, go with a Dries Van Noten or Dior shawl. You could get fur, or faux fur, and look like you're straight off the runway.
If on a budget, Urban Outfitters makes great looking scarves. These are more for a great look, rather than for warmth. Some are heavy enough to be warm, although they look so great you'll be happy with spending only $30 or so, rather than hundreds.