When I make a mushroom based soup ( like mushroom barley), I'll often use a brown roux ( as mentioned above) to kinda give it that added flavor and slightly thicken it uo a bit.
When Im making a minestrone or a tomato based soup that I want to be more hearty than brothy, Ill often take a cup or so of beans , add some broth, blend them into a puree then add to the soup, to give it a thicker, heartier taste and feel.
My grandmother passed down a recipe that she made back in the day. Its a take on mushroom barley, but the soup base has a cup of split yellow peas in it. As they cook down, it thickens the soup (as split green peas would to do pea soup). Its not as thick as Pea soup due to the amount or yellow peas added, that along with the barley add some heartiness to it.
There's a potato soup I made that was rally good. It was ultimately topped off with heavy cream which really did the trick. Now that my wife is vegan, and I have to accommodate, its very difficult ( or impossible) to mimic the heavy cream feel and taste. I can use stuff that is " white" or thicken it with a not so dark roux and it will look right, and not taste bad, but so far I haven't found anything to replace heavy cream. Coconut milk is the closest thing to vegan cream Iv experienced but the coconut taste limits what foods/ soups I can use it in.
When I come across veggie soups that require starting off with frying up some bacon, Ill often just add a few drops of liquid smoke to give it that smokey like taste to it.
This is another one, my daughter loves. We call it 'Bread Soup'
Basically a Tomato based soup, but towards the end you toss in some cubed sourdough, or some other kinda rustic bread in it, which absorb and thicken the soup, but stay together enough to enjoy while eating ( they sop up the soup base adding a nice texture). What I also do in this soup, since my daughter is not a vegan, is toss in a Parmesan Rind towards the end, but I cube it in like 1/4 - 1/2 in cubes. They meld down enough to be soft and chewy. My daughter fishes those pieces out from the pot leaving no for anyone else. ( I go for the bread cubes)
http://www.foodnetwork.com/recipes/ina-garten/ribollita-recipe.html