When should I use a semicolon after curly braces?

It matters too when you intend to minify your code.

So I personally add one after every } where automatic semicolon insertion (ASI) would insert one.

I wrote a post about ASI in JavaScript.

You use a semicolon after a statement. This is a statement:

var foo = function() {
  alert("bar");
};

because it is a variable assignment (i.e. creating and assigning an anonymous function to a variable).

The two things that spring to mind that aren't statements are function declarations:

function foo() {
  alert("bar");
}

and blocks:

{
  alert("foo");
}

Note: that same block construct without semi-colon also applies to for, do and while loops.

Don't use a semicolon:

...if it's just your every-day function declaration:

function foo() {

} // No semicolon

...if it's an assignment:

var foo = function() {

}; // Semicolon

...or a self invoking function:

(function () {

})(); // Semicolon