A plague ravages the kingdom, setting the adventurers on a quest to find a cure. An adventurer emerges from an ancient tomb, unopened for centuries, and soon finds herself suffering from a wasting illness. A warlock offends some dark power and contracts a strange affliction that spreads whenever he casts spells.
A simple outbreak might amount to little more than a small drain on party resources, curable by a casting of lesser restoration. A more complicated outbreak can form the basis of one or more adventures as characters search for a cure, stop the spread of the disease, and deal with the consequences.
A disease that does more than infect a few party members is primarily a plot device. The rules help describe the effects of the disease and how it can be cured, but the specifics of how a disease works aren’t bound by a common set of rules. Diseases can affect any creature, and a given illness might or might not pass from one race or kind of creature to another. A plague might affect only constructs or undead, or sweep through a halfling neighborhood but leave other races untouched. What matters is the story you want to tell.