I've read that adding cork (from wine bottles) absorbs the fat. I'm not sure if this works or not.
Are there any other ways to remove excess fat without standing there and spooning out or refrigerating and then removing the solidified fat?
If you want to be really lazy about it, just get yourself a fat separator. Pour in the soup, the fat will rise to the top, and you can do what you want with it (i.e. dump it).
If you're reading this in an emergency, you can do this with just a strainer. You'll get better results if you chill the strainer before each skim, i.e. by rinsing it with very cold water. The fat will tend to congeal on the cold strainer the same way it congeals when it's actually chilled.
I've also heard that the fat will cling to certain leafy vegetables, like lettuce. If you have a lettuce head kicking around, try peeling off a leaf and dusting the top of the pan with it.
If you pour the liquid into a narrower vessel to settle, the fat layer on top will be thicker and therefore easier to remove with spoon, paper towel, or turkey baster. Something like this thermos or this ice tea jug would work without needing to cool it down too much.
It is best done before any thickening with starch/flour.
Since some spices are oil soluble, you might end up straining out some of the flavor, and need to re-adjust the spicing slightly.
Not to be contrarian, but the easiest way to do this would probably be to just drain off the fat before adding the liquid. For instance, if you sautee your veggies and brown your meat before adding the stock, you'd just pour off the grease in the pan before adding the stock. An ounce of prevention, etc...
If the soup or stew has a good layer of fat on top, I've just dropped individual sheets of paper towels on top. Since the fat is on top, the paper towel absorbs it. Remove, discard and, if there's still a layer of fat, repeat.
Once it starts absorbing stock/broth/sauce, then I stop. Usually the fast majority of fat is gone by then.
Now, however, I have a fat separator, which is, essentially, a handled measuring cup with a spout that connects at the base of the cup. I highly recommend spending a few bucks, it's tremendously convenient, especially for someone like me who loves making and eating homemade soups.
You scoop or pour in the liquid from the top of your dish, let it settle, and, like your pot, the fat separates at the top. Since the spout is connected at the bottom, as you pour liquid back into the pot, it pours back the stuff you want, while the fat remains behind. Once you can see the fat level dropping to spout level, you stop, and have almost entirely fat left behind.
It's also a great way to separate out fat from roasting drippings, so you can use the fat to make a roux for gravy, and have the rich de-fatted pan drippings added back to whatever liquid you are going to add.
So long as the liquid isn't being mixed (and bubbling from simmering or boiling counts as being mixed), it'll undergo what they call "type 1 settling", where oil floats to the top, and particulates fall to the bottom.
You can either let it stand in a gravy separator, or just let it come to the top of the pot, and either ue a paper towel, like Darin mentioned, a strainer like Aronut mentioned, or even a frozen bottle of water (which will chill the fat so it sticks to the bottle, where you ca wipe it off then try again).
Personally, I normally use the 'spooning' method, but use a laddle rather than a spoon, so it goes much faster.