When I need to declare a new array I use this notation
var arr = new Array();
But when testing online, for example on jsbin, a warning sign
Mostly, people use var a = [] because Douglas Crockford says so.
His reasons include the non-intuitive and inconsistent behaviour of new Array():
var a = new Array(5); // an array pre-sized to 5 elements long
var b = new Array(5, 10); // an array with two elements in it
Note that there's no way with new Array() to create an array with just one pre-specified number element in it!
Using [] is actually more efficient, and safer too! It's possible to overwrite the Array constructor and make it do odd things, but you can't overwrite the behaviour of [].
Personally, I always use the [] syntax, and similarly always use {} syntax in place of new Object().