If it's spaced out evenly throughout the day, it's probably not dangerous. I take Adderall and am thirsty a lot, so I probably get close to a gallon a day.
Look out for water intoxication, though, especially while exercising.
I have a school friend who does this. She is a hard core exerciser health person and carries a gallon jug with her to class...I don't think it's normal though. I don't think I drink a gallon of any beverage a day.
It's healthier than drinking tons of soda, but you may still be drinking too much water. I wouldn't really say it's normal, considering how many people I see chugging Gatorade, but there's nothing wrong with it.