Commercially speaking I believe Ripley's in Myrtle Beach has the biggest single standing tank. It's around 380,000 gallons. Lots of commercial aquariums advertise 1+ million gallon aquariums but they are talking about how much total water is in their whole facility. Not just one tank. No obviously SeaWorld has bigger tanks to hold their Orcas and stuff, but for an actual show tank I'm sure Ripley's is it. Underwater World at the Mall of America comes in close behind with 320,000 gallons.
As for established reef tanks I'd have to say Mr4000 is the biggest I know of. As for in home fish tanks I've heard rumors of a guy somewhere in Westchester area of New York with a 140,000 gallon tank but it's never been confirmed. Once my new house is built and my 3 tanks get fully functional and setup, I will have the largest private collection of sharks in the world. Just passing Underwater World at the Mall of America by 12 sharks.
Jim