A list of non-flowering plants would include ferns, algae, rusts and smuts, slime molds, bread molds, mildew and yeast. Non-flowering plants also include truffles, morels and earth tongues. There are also jelly fungi like caloceras, tremellas and coral, tooth and leather fungi.
Other non-flowering plants include mushrooms like amanitas, russulas, mycenas, clitocybes, lactarius and agaricus. Puffballs, stinkhorns, earthstars and bird's nest fungi are also non-flowering plants. Cycads are also ancient, non-flowering plants that look like palm trees.
Because these plants don't flower, most reproduce by way of spores. More information regarding these plants can be found on multiple plant and botany sites.