We've already gone over the classic French sauces and using cornstarch as a thickener. Another method to make thick sauce that my family has enjoyed is to use beans as a thickening agent. Beans add a different texture to the sauce that can convert familiar flavors into something brand new. The following recipe is a good example:
Roasted Chicken Breast with Cheddar-Jalapeno Quesadilla and Spicy Black Bean Sauce
As usual, the recipe has to be adjusted to the patient. If cheddar cheese doesn't work, substitute some other cheese that melts well. The alternatives might include Monterray Jack, mozzarella or cheese food product. We have found store brand mozzarella to be great in Mexican food, and it has the stamp of approval from no less than Marcela Valladolid as a substitute for Oaxaca cheese. As a side note, Marcela comes across as kind of a lightweight on her TV show, but I have seen her on Chopped and she is actually a seriously talented cook.
You can leave out the jalapenos if heat is a problem for you. We've found that canned green chilis are considerably milder. If tomatoes are a problem, you can add some combination of shallots, scallions and peppers. Since you're already an expert with black beans, thanks to this blog, you might want to try simply using your personal black bean recipe adding water or chicken stock as needed to make the puree thin enough to use as sauce. Some extra ingredients might include oregano, cilantro, red pepper flakes, chicken base (one of my personal faves), hot sauce, a pinch of chili powder, thyme, toasted cumin seeds, or coriander.
And that's just for Latin cooking. You can apply any ethnic pallet to a bean sauce: Indian, Chinese, Middle Eastern, or whatever fits the style you are going for at the moment. Just two hints - 1) rinse the beans in a collander or seive before cooking (or one at a time by hand if you have nothing better to do); and 2) cook them low and slow for as long as practical to minimize the canned taste and maximize the opportunity for the ingredients to become friends with eachother.