Aseroe rubra, growing in mulch made from tree branches. The star-shaped red portion mimics rotting flesh, as does the odour of amines (putrescine and cadaverine?) given off the fruiting body. It attracts flies to the black portion in the photo. This is a mass of spores embedded in a sticky matrix. Presumably the spores are spread to other growing areas when they stick to the flies. There is an interesting Wiki article on this fungus, the first one to be recorded in Australia. 
The fly-attracting fruiting body of this fungus and the angiosperm flowers of the genus Stapelia provide an extraordinary example of parallel evolution. They have both evolved a shape and smell of rotting meat to have their spores (pollinia in the case of Stapelia) dispersed by flies.

This is Amanita muscaria, the fly agaric. It is not native to Australia, but seems to have been introduced from the northern hemisphere on the roots of imported trees. On our site, it grows close to a line of radiata pine, with which it has a symbiotic relationship. You can find many interesting facts on this fungal fly killer on this Wiki page.

The shaggy cap Coprinus comatus, taken in late May. While apparently native to Australia, it has a wide distribution in both northern and southern hemispheres. It is often suggested that alcohol will cause unpleasant symptoms if consumed with this fungus. However, there is some doubt whether the chemical responsible, coprine, is present in Coprinus comatus. Caution is required, however, because there are several other species of Coprinus in Australia. Symptoms of poisoning are described in this link.

Above is the beautifully luminescent fungus Omphalotus nidiformis. I first saw this one pitch-dark night after dinner in a Sydney suburb, when the host took me and other guests into the nearby bush. It appears quite commonly after damp weather, but the luminescence is only bright when the caps are young. It is definitely poisonous to eat - more details on this Wiki page.