Archaebacteria, more properly called archaea, are single celled organisms that live in a wide range of habitats, including the harsh conditions of hot springs. Thermophiles are arachea which grow best at temperatures above 45 Celsius, but some species thrive in much warmer temperatures. According to Reference.com, "Methanopyrus kandleri Strain 116 grows at 122 °C, which is the highest recorded temperature at which any organism will grow."
Other members of this group live in conditions that are very acidic or very alkaline. Picrophilus torridus as one of the most extreme archaean acidophiles. This organism grows at a pH 0, which Reference.com equates this to 1.2 Molar sulfuric acid.
Thermoacidophiles thrive in hot environments that are also acidic, with a pH between 1 and 5. These conditions exist in hydrothermal vents and acidic hot springs, according to About.com.
Halophiles live in environments too salty for other organisms to survive. Reference.com reports that they begin to outnumber the bacterial counterparts once salinity reaches 20 to 25 percent.
Archaea were originally seen only as extremophiles and as only living in harsh environments. However, scientists also find them in a broad range of habitats. They live in oceans, soils and marshlands. Reference.com says the archaea in plankton are possibly "one of the most abundant groups of organisms on the planet."