What illness could cause tooth discoloration?

Illnesses in mothers: Infections in pregnant mothers can cause intrinsic (on the inside of the tooth) discoloration in their offspring by effecting the enamel as it develops. Certain drugs taken by preganant mothers can also cause discoloration of their childs teeth such as takeing tetracycline during preganancy. Illness can sometimes result in extrinsic staining (on the outside) because it effects dental hygiene.

Tetracycline : Taking tetracycline antibiotic while the teeth are developing can cause discoloration. Usually patients will require veneers for whiter teeth.

Many: Any incidence of high fever during tooth development can cause tooth discoloration. Usually blotchy white spots.

Tooth discoloration?: Many possibilities. High fever during development of tooth, too much systemic fluoridation, use of tetracycline during tooth formation, local infection during tooth development, death of contents of canals in tooth from trauma or decay.

Tooth discoloration: In addition to causes noted in Dr. Sandler's excellent answer, please add poor oral hygiene, chromogenic (pigment producing) bacteria, many foods (coffee/tea/tomato sauce/saffron/etc.), staining of fractures caused by eating ice/hard candy/etc., Betel Nuts, failure to have regular (6 month) professional cleanings, smoking (anything), smokeless tobacco use, and so many other possibilities.