sickness / illness / disease / malady / ailment / indisposition

SICKNESS is the common, everyday word.  ILLNESS is a more formal word and is often attached to more serious sicknesses. 
Though in its origin, DISEASE meant any deviation from a state of ease, it now designates an organic deviation involving structural change, serious, active, prolonged and deep-rooted.
A MALADY is a lingering, chronic disease, usually painful and often fatal.
AILMENT is often used lightly to describe some minor affliction, but it may also be used of something more serious, especially when the exact nature of the sicknes is not known to the speaker.
INDISPOSITION is a rather ponderous euphemism for sickness.  It is often preceded by slight and is never used of a serious sickness.
 
from A Dictionary of Contemporary American Usage (Random House, 8th Printing 1957) by Bergen Evans and Cornelia Evans