Short Answer

Use $this to refer to the current object. Use self to refer to the current class. In other words, use $this->member for non-static members, use self::$member for static members.

Full Answer

Here is an example of correct usage of $this and self for non-static and static member variables:

<?php
class X {
    private $non_static_member = 1;
    private static $static_member = 2;

    function __construct() {
        echo $this->non_static_member . ' '
           . self::$static_member;
    }
}

new X();
?>

Here is an example of incorrect usage of $this and self for non-static and static member variables:

<?php
class X {
    private $non_static_member = 1;
    private static $static_member = 2;

    function __construct() {
        echo self::$non_static_member . ' '
           . $this->static_member;
    }
}

new X();
?>

Here is an example of polymorphism with $this for member functions:

<?php
class X {
    function foo() {
        echo 'X::foo()';
    }

    function bar() {
        $this->foo();
    }
}

class Y extends X {
    function foo() {
        echo 'Y::foo()';
    }
}

$x = new Y();
$x->bar();
?>

Here is an example of suppressing polymorphic behaviour by using self for member functions:

<?php
class X {
    function foo() {
        echo 'X::foo()';
    }

    function bar() {
        self::foo();
    }
}

class Y extends X {
    function foo() {
        echo 'Y::foo()';
    }
}

$x = new Y();
$x->bar();
?>

The idea is that $this->foo() calls the foo() member function of whatever is the exact type of the current object. If the object is of type X, it thus calls X::foo(). If the object is of type Y, it calls Y::foo(). But with self::foo(), X::foo() is always called.

From http://www.phpbuilder.com/board/showthread.php?t=10354489:

By http://board.phpbuilder.com/member.php?145249-laserlight

Depending upon use case, I would normally use something simple like the following:

abstract class DaysOfWeek
{
    const Sunday = 0;
    const Monday = 1;
    // etc.
}

$today = DaysOfWeek::Sunday;

However, other use cases may require more validation of constants and values. Based on the comments below about reflection, and a few other notes, here's an expanded example which may better serve a much wider range of cases:

abstract class BasicEnum {
    private static $constCacheArray = NULL;

    private static function getConstants() {
        if (self::$constCacheArray == NULL) {
            self::$constCacheArray = [];
        }
        $calledClass = get_called_class();
        if (!array_key_exists($calledClass, self::$constCacheArray)) {
            $reflect = new ReflectionClass($calledClass);
            self::$constCacheArray[$calledClass] = $reflect->getConstants();
        }
        return self::$constCacheArray[$calledClass];
    }

    public static function isValidName($name, $strict = false) {
        $constants = self::getConstants();

        if ($strict) {
            return array_key_exists($name, $constants);
        }

        $keys = array_map('strtolower', array_keys($constants));
        return in_array(strtolower($name), $keys);
    }

    public static function isValidValue($value, $strict = true) {
        $values = array_values(self::getConstants());
        return in_array($value, $values, $strict);
    }
}

By creating a simple enum class that extends BasicEnum, you now have the ability to use methods thusly for simple input validation:

abstract class DaysOfWeek extends BasicEnum {
    const Sunday = 0;
    const Monday = 1;
    const Tuesday = 2;
    const Wednesday = 3;
    const Thursday = 4;
    const Friday = 5;
    const Saturday = 6;
}

DaysOfWeek::isValidName('Humpday');                  // false
DaysOfWeek::isValidName('Monday');                   // true
DaysOfWeek::isValidName('monday');                   // true
DaysOfWeek::isValidName('monday', $strict = true);   // false
DaysOfWeek::isValidName(0);                          // false

DaysOfWeek::isValidValue(0);                         // true
DaysOfWeek::isValidValue(5);                         // true
DaysOfWeek::isValidValue(7);                         // false
DaysOfWeek::isValidValue('Friday');                  // false

As a side note, any time I use reflection at least once on a static/const class where the data won't change (such as in an enum), I cache the results of those reflection calls, since using fresh reflection objects each time will eventually have a noticeable performance impact (Stored in an assocciative array for multiple enums).

Now that most people have finally upgraded to at least 5.3, and SplEnum is available, that is certainly a viable option as well--as long as you don't mind the traditionally unintuitive notion of having actual enum instantiations throughout your codebase. In the above example, BasicEnum and DaysOfWeek cannot be instantiated at all, nor should they be.