function read_file(file, delete_after) {
    delete_after = delete_after || "my default here";
    //rest of code
}

This assigns to delete_after the value of delete_after if it is not a falsey value otherwise it assigns the string "my default here". For more detail, check out Doug Crockford's survey of the language and check out the section on Operators.

This approach does not work if you want to pass in a falsey value i.e. false, null, undefined, 0 or "". If you require falsey values to be passed in you would need to use the method in Tom Ritter's answer.

When dealing with a number of parameters to a function, it is often useful to allow the consumer to pass the parameter arguments in an object and then merge these values with an object that contains the default values for the function

function read_file(values) {
    values = merge({ 
        delete_after : "my default here"
    }, values || {});

    // rest of code
}

// simple implementation based on $.extend() from jQuery
function merge() {
    var obj, name, copy,
        target = arguments[0] || {},
        i = 1,
        length = arguments.length;

    for (; i < length; i++) {
        if ((obj = arguments[i]) != null) {
            for (name in obj) {
                copy = obj[name];

                if (target === copy) {
                    continue;
                }
                else if (copy !== undefined) {
                    target[name] = copy;
                }
            }
        }
    }

    return target;
};

to use

// will use the default delete_after value
read_file({ file: "my file" }); 

// will override default delete_after value
read_file({ file: "my file", delete_after: "my value" }); 

ES2015 onwards:

From ES6/ES2015, we have default parameters in the language specification. So we can just do something simple like,

function A(a, b = 4, c = 5) {
}

or combined with ES2015 destructuring,

function B({c} = {c: 2}, [d, e] = [3, 4]) {
}

For detailed explanation,

https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Functions/default_parameters

Default function parameters allow formal parameters to be initialized with default values if no value or undefined is passed.

Pre ES2015:

If you're going to handle values which are NOT Numbers, Strings, Boolean, NaN, or null you can simply use

(So, for Objects, Arrays and Functions that you plan never to send null, you can use)

param || DEFAULT_VALUE

for example,

function X(a) {
  a = a || function() {};
}

Though this looks simple and kinda works, this is restrictive and can be an anti-pattern because || operates on all falsy values ("", null, NaN, false, 0) too - which makes this method impossible to assign a param the falsy value passed as the argument.

So, in order to handle only undefined values explicitly, the preferred approach would be,

function C(a, b) {
  a = typeof a === 'undefined' ? DEFAULT_VALUE_A : a;
  b = typeof b === 'undefined' ? DEFAULT_VALUE_B : b;
}