The answer to the riddle "what can you catch but not throw" is "a cold." The riddle is a play on colloquial verbiage when someone "catches a cold," meaning someone is infected with a rhinovirus that affects the sinus, nasal and breathing pathways in a human being.
In the United States, about 1 billion colds occur annually with an economic loss of $20 billion due to work loss. Between 75 and 100 million doctors' visits are recorded every year due to common colds. The common cold is caused by as many as 200 viruses, with the rhinovirus accounting for 30 to 35 percent of the colds in adults.