I've used oats as a thickener in savory dips (roasted red pepper & feta), they disappear in the food processor. Here's another idea to use it in soup (pureed):

http://kahakaikitchen.blogspot.com/2009/05/potage-of-asparagus-white-wine-lemon-or.html

there's always haggis!

I use oatmeal in savory recipes! Besides the more obvious applications of using it to thicken stews and soups, I also have a favorite oatmeal fritter that I like to make. Here is my recipe:

1 cup old fashioned oatmeal
1 medium onion, finely diced
1/2 cup parsley, finely minced
3/4 cup boiled water
1 jalapeno pepper, finely minced
1/3 cup celery, finely diced
sea salt to taste
coarse ground pepper

vegetable oil for frying

Heat 2 inches of vegetable oil to 350 degrees. Mix all the other ingredients until well combined. Fry heaping tablespoons of the mixture in the hot oil until golden and slightly puffed.

Mark Bittman uses rolled oats in his veggie burger recipes, I believe. They're all in "How to Cook Everything Vegetarian"

He also has a savory oatmeal recipe that sounds kind of interesting.

My mom always put oatmeal in meatloaf instead of bread crumbs. I like the chewy texture.

I do meatloaf with oats instead of bread crumbs...here's one recipe:

http://naturalwholefoodrecipes.wordpress.com/2009/12/24/gourmet-turkey-meatloaf/

I do endless variations on the theme and of course use beef as well as turkey.

My mom uses a little oatmeal as a filler for chinese dumplings (and yes, she is actually Chinese!)

I did this the other day. I have a vegetarian chili recipe that calls for a cup of barley, and I only had 1/4 cup or so left, so I made up the difference with oatmeal. I didn't even notice a difference in the final product.

i also use oats instead of breadcrumbs in turkey meatloaf. i lightly moisten them with some soy or Worcestershire sauce so they take on a meaty flavor.

i use whole oat groats for this recipe:
http://beetgoeson.blogspot.com/2008/12/avena-con-setas.html

and, like others here, as a replacement for breadcrumbs in meatloaf or meatballs.

Steel cut oats can have a texture very much like rice or bulgar wheat, depending on how you cook it. I prefer my oats firmer, so I cook them using Alton Brown's method - you start by toasting the oats in a little butter, then add boiling water and simmer for about 25 minutes. I cook them half with the lid on, half off, to give them a firmer texture. Finally add buttermilk or milk, and cook another 10 minutes. The oats come out a bit like risotto, and I've been known to add bacon or chicken or mushrooms and turn it into a main course. I never liked oatmeal until I had it this way.

Use it, instead of flour, to coat chicken before frying it. It's absolutely delicious.

The Quakers oats boxes in India come with a "Poha" recipe. Poha is a savory breakfast dish made of flattened rice. The quaker box says to replace flattened rice with oats. Haven't tried it but intend to. Here's a poha recipe from an older Kitchn post.
http://www.thekitchn.com/thekitchn/breakfast/recipe-breakfast-poha-047062

Hey...Wondered the same thing couple of weeks back...Came up with oatmeal soup!!! Me and hubbie don't always like to have a cold, sweet breakfast..So this is quickie soup which is also great as a spread on thick, toasted bread when cooled...

1/2 cup oatmeal
finely chopped cabbage
finely chopped carrots
mushrooms (optional)
ground pepper (white/black, whatever u can get ur hands on early in the morning!!!)
finely chopped spring onions (the greens add a nice color)
Garlic and garlic paste (1/4th teaspoon)
Oil to cook
Salt to taste
2 cups water

Saute the chopped onions and ginger, garlic paste till onions turn translucent. Add salt and veggies, turn the flame to simmer for 10 mins. Meanwhile, stew oats with water in a separate container, till the broth turns thick (You can adjust the amount of water needed according to the consistency. When the veggies are soft, mix with the oats broth. Garnish with pepper and chopped spring onions.

You can also let the veggies and oats stew together in water, instead of doing separately. But I feel the veggies turn bland when boiled with water.