In biological taxonomy, mildew (Family: Peronosporaceae, genus Erysiphe, Peronospora; is the type of fungi that form a superficial, usually whitish growth on plants and various organic materials.

Phylum: Mastigomycota
class Oomycetes
order Peronosporales
genus Peronospora
    blue mold fungus
    mildew (tobaco, onion)
genus ?
    powerdy mildew

subdivision/Subphylum Ascomycotina
class Plectomycetes
order Aspergillales
genus Aspergillus

Phylum:Deuteromycota
Subphylum:Pezizomycotina
Class:Eurotiomycetes
Order:Eurotiales
Family:Trichocomaceae
Genus:Aspergillus

Downy mildew (Phylum: Oomycota in the Kingdom PROTISTA)

Powdery mildew - (Phylum: Ascomycota in the Kingdom FUNGI) 

Mold:  (Phylum: Ascomycota in the Kingdom FUNGI)

Subphylum: Ascomycotina
Genus: Cladosporium

class Hyphomycetes of the subdivision Deuteromycotina,
such as Penicillium, Aspergillus, Cladosporium, and Stachybotrys

Stachybotrys  Aspergillus Cladosporium Stachybotrys

Mold can grow on almost any substance as long as it has a carbon-based food source, moisture, oxygen, and the temperature is between 40 and 100° F.

Most molds reproduce by forming spores that disperse into the air in search of more food and moisture (a reproductive activity similar to seed dispersal from plants). Due to the diversity of mold in our environment, outdoor air normally always contains some level of these airborne mold spores.

Mold growing on glass, ceramic tile, metals, or other inorganic materials is not obtaining nutrients from these substrates. In these cases, mold is feeding on microscopic organic matter that is on the surface or trapped in tiny pores of the material. Bath-tile mold is an example: Mold is typically consuming organic dust, dirt, debris, skin flakes, body oils, soap scum, etc., and the ceramic tile is simply a foundation for the colony.

Mold has been implicated as a major cause of Building Related Illness (BRI) and Sick Building Syndrome (SBS). Studies have shown that exposure to indoor mold can induce respiratory illness in adults, and can cause early onset asthma and allergies in children.

Mold: (Phylum: Ascomycota)

Genus	Characteristics
Alternaria	A large spore mold that can deposit in the nose, mouth and upper respiratory tract causing an allergic response. Indoors, it is often found in carpets, textiles, house dust and potentially damp areas like window frames and showers. It can also be found in plant soil.
Aspergillus	Usually found in warmer climates in areas of water damage or extreme dampness. Aspergillus species are also commonly found in house dust. Many species produce mycotoxins which may be associated with disease in humans and some animals. Also found in building materials and in fall leaves and other decomposing matter like compost piles.
Cladosporium	The most commonly identified outdoor fungus, but it can easily enter into the house through the HVAC and other airflow entryways. Cladosporium also has an indoor species that grows on textiles, wood and other porous, damp areas. Both indoor and outdoor species are triggers for hay fever and asthma symptoms.
Penicillium	A very common mold known to cause allergies, hay fever and asthma. Species may be found growing on wallpaper, wallpaper glue and decaying fabrics in water-damaged buildings or homes. It is also found in carpet and in interior fiberglass duct insulation. Some species can produce mycotoxins.
Stachybotrys	Pronounced (stack-ee-BOT-ris), this is an especially toxic black mold that produces airborne toxins (mycotoxins) that can cause serious breathing difficulties, memory and hearing loss, dizziness, flu-like symptoms and bleeding in the lungs. Stachybotrys requires excessive moisture to thrive (usually running water) and is a slimy black mold. Fortunately, stachybotrys is not found in homes as often as the other molds listed above.

Source: Indoor Air Quality and Your Health at National Allergy

Table 2. Common types of moldy and decay fungi in buildings

See:
About Mold
Indoor Air Quality and your health.