Is it harmful to drink 24 cups of water a day?

Yes: Drinking 24 cups (assuming 8 oz cups) of water a day is a lot of water, and would likely wash too much sodium out of one's body. If a person has some special reason for drinking this much water, he should get evaluated by his doctor, who can assess the reason, as well as check urine and blood chemistries to see if the electrolytes (sodium, potassium, chloride, etc...) are dangerously abnormal.

Probably not: The usual feeling is that 8 cups of liquid per day is sufficient. 24 cups would obligate you to never be far from a bathroom and unless you have an unusual problem with water metabolism, you body will simply eliminate the excess water with an outpouring of diluted urine. If you are doing this as part of a detox regimen, it is doubtful that over 8 cups will add anything.