Fungi like yeast reproduce by budding. Hydra, a simple Cnidaria, can carry out budding as well. Other fungi produce spores, like in bread mold, which makes hundreds of new, identical molds, that are just like the parent that produced the spores. Starfish can lose a limb and by regeneration, the missing limb can grow into a new starfish. Protists are capable of cell division which is asexual reproduction. Pieces of plants-roots, stems or leaves can be used as cuttings to form new offspring asexually.
All bacteria are considered to be asexual. While some species can exchange genetic material, it is not required for reproduction.
A number of species can reproduce either sexually or asexually; this is true of many plant species, as well as hydras, sponges, planarians, amoebas, ants, bees, and fungi.