When I took these pictures I thought the top two were quite different from each other and from the bottom two. But, when I walked past them the next day, they looked just like the one on the bottom left. As it turns out, they're all the same slime mold: Fuligo septica. The pictures (left to right, top to bottom) show different life stages of the plasmodium (reproductive structure). The common name for this is, appropriately enough, the "dog vomit slime mold".
Next up are bird's nest fungi (Family Nidulariaceae), which are true fungi. I've seen these in Utah and Wyoming, too, but not nearly so abundantly. Their common name comes from the fact that they look like little bowls with eggs in them. The eggs (called peridioles) are usually ejected from the nests (called peridia) by rainfall.
Then we have these, which are called chicken of the woods (Laetiporus cincinnatus). They kind of look like an orange lettuce or coral. These are edible and derive their name from the fact that most people think they taste like chicken (a minority think they taste more like lobster or crab).
These are shelf fungi I spotted the scar of a removed branch on a tree in the University of Wisconsin–Madison Arboretum. It was too far up to get a good look at, so I'm unable to identify it any further. The plant with purple berries that you can see growing above the fungi, in the crotch of the cut-off branch, is not part of the original tree.
Other fungi I've seen, but don't have photographs for: the artist's bracket (Ganoderma applanatum) the mower's mushroom (Panaeolus foenisecii), the white dunce cap (Conocybe apala), the dog stinkhorn (Mutinus caninus), and the common ink cap (Coprinopsis atramentaria).
 I know people pick (and sell) edible morel mushrooms around here, but I've yet to see any.
 See http://en.wikipedia.org/wiki/Fuligo septica.
 See http://en.wikipedia.org/wiki/Nidulariaceae.
 See http://en.wikipedia.org/wiki/Laetiporus cincinnatus.
 This seems like a pretty good visual tour of some common Eastern mushrooms.