This only really talks about soil, but damping off can also occur in hydro systems that use a water culture.
Damping-off
The single term used to describe underground, soil line, or crown rots of seedlings due to unknown causes is damping-off . The term actually covers several soil borne diseases of plants and seed borne fungi.
Rhizoctonia root rot (Rhizoctonia solani) is a fungal disease which causes damping-off of seedlings and foot rot of cuttings. Infection occurs in warm to hot temperatures and moderate moisture levels. The fungi is found in all natural soils and can survive indefinitely. Infected plants often have slightly sunken lesions on the stem at or below the soil line. Transfer of the fungi to the germination room or greenhouse is easily accomplished by using outdoor gardening tools inside or vice versa. The germination room should not be used for mixing potting soils or transplanting seedlings as a general rule.
Pythium Root Rot (Pythium spp.) is similar to Rhizoctonia in that it causes damping-off of seedlings and foot rot of cuttings. However, infection occurs in cool, wet, poorly-drained soils, and by overwatering. Infection results in wet odorless rots. When severe, the lower portion of the stem can become slimy and black. Usually, the soft to slimy rotted outer portion of the root can be easily separated from the inner core. Species of Pythium can survive for several years in soil and plant refuse.
Phytophthora root rot (Phytophthora spp.) are usually associated with root rots of established plants but are also involved in damping-off. These species enter the root tips and cause a water-soaked brown to black rot similar to Pythium. These fungi survive indefinitely in soil and plant debris.
Black root rot (Thielaviopsis basicola) is a problem of established plants. It does not occur in strongly acid soils with a pH of 4.5 to 5.5. It usually infects the lateral roots where they just emerge from the taproot. The diseased area turns dark brown, and is quite dry. The fungi survive for 10 years or more in soil.
Miscellaneous fungi causing similar symptoms include Sclerotinia (white mold), Sclerotium rolfsii, Macrophomina phaseoli, some species of Botrytis (gray mold), Aphonomyces, Fusarium, Cylindrocladium, and others. Hence the need for the collective term known as damping-off.