Why 750 mL bottles of wine?

In the United States, wine may only be sold in 750 mL bottles, or certain standard fractions and multiples of 750 mL. This law was passed in 1979, back when America was "going metric" withing 10 years of the Metric Conversion Act of 1975. European wine bottles had varied in size, but they were standardized in order to match the American 750 mL standard.

Why did we opt for 750 mL instead of one liter or 500mL, in which we bottle water?

The 750 mL bottle was chosen because it is close to the traditional "fifth" in which liquor was sold in the US.

So why package liquor in fifths of gallons? Why not quarts?  

Here's a great explanation:

"The fifth had been invented by the spirits industry many years before to avoid being taxed, since taxes were assessed for quarts or larger volumes of wine or spirits."
 http://humboldtartisanwineguild.com/Wine%20Bottles.pdf

Apparently, this was a great loophole in the tax law. Bottlers who sold quantities of gallons and quarts had to pay excise taxes. So for a while, fifths were tax free!

People began to expect their liquor in fifths. Now we buy wine in 750 mL bottles. And so does the rest of the world!