Instead of this:
<?php setcookie( "TestCookie", $value, time()+(60*60*24*30) ); ?>

You can this:
<?php setcookie( "TestCookie", $value, strtotime( '+30 days' ) ); ?>

Want to remove a cookie?

Many people do it the complicated way:
setcookie('name', 'content', time()-3600);

But why do you make it so complicated and risk it not working, when the client's time is wrong? Why fiddle around with time();

Here's the easiest way to unset a cookie:
setcookie('name', 'content', 1);

Thats it.

Just an example to clarify the use of the array options, especially since Mozilla is going to deprecate / penalise the use of SameSite = none,  which is used by default if not using array options. 

<?php
$arr_cookie_options = array (
                'expires' => time() + 60*60*24*30, 
                'path' => '/', 
                'domain' => '.example.com', // leading dot for compatibility or use subdomain
                'secure' => true,     // or false
                'httponly' => true,    // or false
                'samesite' => 'None' // None || Lax  || Strict
                );
setcookie('TestCookie', 'The Cookie Value', $arr_cookie_options);    
?>

It's worth a mention: you should avoid dots on cookie names.

<?php
// this will actually set 'ace_fontSize' name:
setcookie( 'ace.fontSize', 18 );
?>

Note when setting "array cookies" that a separate cookie is set for each element of the array.

On high traffic sites, this can substantially increase the size of subsequent HTTP requests from clients (including requests for static content on the same domain).

More importantly though, the cookie specification says that browsers need only accept 20 cookies per domain.  This limit is increased to 50 by Firefox, and to 30 by Opera, but IE6 and IE7 enforce the limit of 20 cookie per domain.  Any cookies beyond this limit will either knock out an older cookie or be ignored/rejected by the browser.

something that wasn't made clear to me here and totally confused me for a while was that domain names must contain at least two dots (.), hence 'localhost' is invalid and the browser will refuse to set the cookie! instead for localhost you should use false.

to make your code work on both localhost and a proper domain, you can do this:

<?php

$domain = ($_SERVER['HTTP_HOST'] != 'localhost') ? $_SERVER['HTTP_HOST'] : false;
setcookie('cookiename', 'data', time()+60*60*24*365, '/', $domain, false);

?>

In any web browser there is a very commonly used option "Open previous windows and tabs" which is disabled by default, but many people enable it.
When this option is active, the web browser, when closing and reopening, instead of executing the termination and starting a new session, saves and restores the current session along with session cookies and sessionStorage.
Both session cookies and sessionStorage, contrary to expectations, can live for a very long time until the user closes the tab before closing the web browser.
If you want a cookie, for example with a time offset, to be guaranteed to have a short lifetime, you should explicitly specify this short lifetime, rather than relying on self-deletion on the session cookie.

If you want to delete all cookies on your domain, you may want to use the value of:

<?php $_SERVER['HTTP_COOKIE'] ?>

rather than:

<?php $_COOKIE ?>

to dertermine the cookie names. 
If cookie names are in Array notation, eg: user[username] 
Then PHP will automatically create a corresponding array in $_COOKIE. Instead use $_SERVER['HTTP_COOKIE'] as it mirrors the actual HTTP Request header. 

<?php

// unset cookies
if (isset($_SERVER['HTTP_COOKIE'])) {
    $cookies = explode(';', $_SERVER['HTTP_COOKIE']);
    foreach($cookies as $cookie) {
        $parts = explode('=', $cookie);
        $name = trim($parts[0]);
        setcookie($name, '', time()-1000);
        setcookie($name, '', time()-1000, '/');
    }
}

?>

The " PHPSESSID " cookie will soon be rejected because its " sameSite " attribute is set to " none " or an invalid value, and without " secure " attribute. To learn more about the "sameSite" attribute, visit https://developer.mozilla.org/docs/Web/HTTP/Headers/Set-Cookie/SameSite.

<?php
 ini_set("session.cookie_secure", 1);
 session_start();

my PHP code .... 

?>

Caveat: if you use URL RewriteRules to get stuff like this: domain.com/bla/stuf/etc into parameters, you might run into a hickup when setting cookies.
At least in my setup a change in one of the parameters resulted in the cookie not being 'there' anymore.
The fix is simple: specify the domain. '/' will usualy do fine.

A period in a cookie name (like user.name) seems to show up in the $_COOKIE array as an underscore (so user_name). This means that for example $_COOKIE["user_name"] must be used to read a cookie that has been set with setcookie("user.name" ...), which is already rather confusing. 

Furthermore the variable $_COOKIE["user_name"] will retain the value set by setcookie("user.name" ...) and no amount of calling setcookie("user_name" ...) will alter this value. This is rather trivially fixed by clearing the "user.name" cookie, but it can take a while to realize this since there's only "user_name" in $_COOKIE.

Hope this saves someone some time.

Note that the $_COOKIE variable not will hold multiple cookies with the same name. It is legitimate to set two cookies with the same name to the same host where the sub domain is different. 
<?php
setcookie("testcookie", "value1hostonly", time(), "/", ".example.com", 0, true);
setcookie("testcookie", "value2subdom", time(), "/", "subdom.example.com", 0, true);
?>
The next request from the browser will have both cookies in the $_SERVER['HTTP_COOKIE'] variable, but only one of them will be found in the $_COOKIE variable. Requests to subdom.example.com will have both cookies, while browser request to example.com or www.example.com only sends the cookie with the "value1hostonly" value.

<?php
$kaker = explode(";", $_SERVER['HTTP_COOKIE']);
foreach($kaker as $val){
    $k = explode("=", $val);
    echo trim($k[0]) . " => " . $k[1];
}

// output
testcookie => value1hostonly
testcookie => value2subdom

?>

Please keep in mind that if you call setcookie() several times during the script execution (even for the same name, domain and path), then Set-Cookie header will be sent several times, and only after receiving all of them, client browser will "merge" them, replacing first value for the cookie with the next etc.

This may cause very large headers length sometimes, so you'll have to either increase buffers for your web server; change your code logic to determine all possibly-changing parameters values right from the start; implement some sort of global Response object keeping all the data, including cookies as well, till the end of processing (sort of optimized output beffering); or just avoid storing any large data in cookies.

As of PHP 7.3, you can use this syntax:

setcookie( $name,  $value,  $options)

Be aware that the array in $options is not fully compatible with array key names. In other words, the order of your array values matters regardless of the array key names.

<?PHP

// Correct (with key names):
setcookie(
    'my_cookie',
    'my_value',
    [
        'expires' => time() + 3600,
        'path' => '/',
    ]
);

// Correct (without key names):
setcookie(
    'my_cookie',
    'my_value',
    [
        time() + 3600, // expires
        '/' // path
    ]
);

// Incorrect Usage (wrong order as key names are ignored):
setcookie(
    'my_cookie',
    'my_value',
    [
        'path' => '/', // WRONG: should be 2nd
        'expires' => time() + 3600, // WRONG: should be 1st
    ]
);

// Here's the correct order of the $options array with default values:
$options = [
    'expires' => 0,
    'path' => "",
    'domain' => "",
    'secure' => false,
    'httponly' => false
];

setcookie(
    'my_cookie',
    'my_value',
    $options 
);

?>

If you do not provide options, the default values will be used.