Passing a parameter to filter and action functions

By default this is not possible. There are workarounds if you do it the OOP way.
You could create a class to store the values you want to use later.

Example:

/**
 * Stores a value and calls any existing function with this value.
 */
class WPSE_Filter_Storage
{
    /**
     * Filled by __construct(). Used by __call().
     *
     * @type mixed Any type you need.
     */
    private $values;

    /**
     * Stores the values for later use.
     *
     * @param  mixed $values
     */
    public function __construct( $values )
    {
        $this->values = $values;
    }

    /**
     * Catches all function calls except __construct().
     *
     * Be aware: Even if the function is called with just one string as an
     * argument it will be sent as an array.
     *
     * @param  string $callback Function name
     * @param  array  $arguments
     * @return mixed
     * @throws InvalidArgumentException
     */
    public function __call( $callback, $arguments )
    {
        if ( is_callable( $callback ) )
            return call_user_func( $callback, $arguments, $this->values );

        // Wrong function called.
        throw new InvalidArgumentException(
            sprintf( 'File: %1$s<br>Line %2$d<br>Not callable: %3$s',
                __FILE__, __LINE__, print_r( $callback, TRUE )
            )
        );
    }
}

Now you can call the class with any function you want – if the function exists somewhere it will be called with your stored parameters.

Let’s create a demo function …

/**
 * Filter function.
 * @param  array $content
 * @param  array $numbers
 * @return string
 */
function wpse_45901_add_numbers( $args, $numbers )
{
    $content = $args[0];
    return $content . '<p>' . implode( ', ', $numbers ) . '</p>';
}

… and use it once …

add_filter(
    'the_content',
    array (
        new WPSE_Filter_Storage( array ( 1, 3, 5 ) ),
        'wpse_45901_add_numbers'
    )
);

… and again …

add_filter(
    'the_content',
    array (
        new WPSE_Filter_Storage( array ( 2, 4, 6 ) ),
        'wpse_45901_add_numbers'
    )
);

Output:

The key is reusability: You can reuse the class (and in our examples also the function).

PHP 5.3+

If you can use a PHP version 5.3 or newer closures will make that much easier:

$param1 = '<p>This works!</p>';
$param2 = 'This works too!';

add_action( 'wp_footer', function() use ( $param1 ) {
        echo $param1;
    }, 11 
);
add_filter( 'the_content', function( $content ) use ( $param2 ) {
        return t5_param_test( $content, $param2 );
    }, 12
);

/**
 * Add a string to post content
 *
 * @param  string $content
 * @param  string $string This is $param2 in our example.
 * @return string
 */
function t5_param_test( $content, $string )
{
    return "$content <p><b>$string</b></p>";
}

The downside is that you cannot write unit tests for closures.