Set a cookie to never expire

Question

All cookies expire as per the cookie specification, so this is not a PHP limitation.

Use a far future date. For example, set a cookie that expires in ten years:

setcookie(
  "CookieName",
  "CookieValue",
  time() + (10 * 365 * 24 * 60 * 60)
);

Note that if you set a date past 2038 in 32-bit PHP, the number will wrap around and you'll get a cookie that expires instantly.

Maximum value: 2147483647

setcookie("CookieName", "CookieValue", 2147483647);

To avoid integer overflow the timestamp should be set to:

2^31 - 1 = 2147483647 = 2038-01-19 04:14:07

Setting a higher value might cause problems with older browsers.

Also see the RFC about cookies:

Max-Age=value
  OPTIONAL.  The value of the Max-Age attribute is delta-seconds,
  the lifetime of the cookie in seconds, a decimal non-negative
  integer.  To handle cached cookies correctly, a client SHOULD
  calculate the age of the cookie according to the age calculation
  rules in the HTTP/1.1 specification [RFC2616].  When the age is
  greater than delta-seconds seconds, the client SHOULD discard the
  cookie.  A value of zero means the cookie SHOULD be discarded
  immediately.

and RFC 2616, 14.6 Age:

If a cache receives a value larger than the largest positive integer it can represent, or if any of its age calculations overflows, it MUST transmit an Age header with a value of 2147483648 (2^31).

http://www.faqs.org/rfcs/rfc2616.html

Set a far future absolute time:

setcookie("CookieName", "CookieValue", 2147483647);

It is better to use an absolute time than calculating it relative to the present as recommended in the accepted answer.

The maximum value compatible with 32 bits systems is:

2147483647 = 2^31 = ~year 2038

My privilege prevents me making my comment on the first post so it will have to go here.

Consideration should be taken into account of 2038 unix bug when setting 20 years in advance from the current date which is suggest as the correct answer above.

Your cookie on January 19, 2018 + (20 years) could well hit 2038 problem depending on the browser and or versions you end up running on.