Boolean(expression) will simply convert the expression into a boolean primitive value, while new Boolean(expression) will create a wrapper object around the converted boolean value.

The difference can be seen with this:

// Note I'm using strict-equals

new Boolean("true") === true; // false

Boolean("true") === true; // true

And also with this (thanks @hobbs):

typeof new Boolean("true"); // "object"

typeof Boolean("true"); // "boolean"

Note: While the wrapper object will get converted to the primitive automatically when necessary (and vice versa), there is only one case I can think of where you would want to use new Boolean, or any of the other wrappers for primitives - if you want to attach properties to a single value. E.g:

var b = new Boolean(true);

b.relatedMessage = "this should be true initially";

alert(b.relatedMessage); // will work

var b = true;

b.relatedMessage = "this should be true initially";

alert(b.relatedMessage); // undefined