How to store widget fields data as an array?

You have to collect multiple fields under the same name like this …

name="collect[1]"
name="collect[2]"

… and adjust your widget logic to this.

Here is a very simple demo widget:

<?php  # -*- coding: utf-8 -*-
/* Plugin Name: Store Options as array */

add_action( 'widgets_init', array ( 'T5_Array_Options_Widget', 'register' ) );

class T5_Array_Options_Widget extends WP_Widget
{
    /**
     * Constructor.
     */
    public function __construct()
    {
        parent::__construct( strtolower( __CLASS__ ), 'Array Demo' );
    }

    /**
     * Echo the settings update form
     *
     * @param array $instance Current settings
     */
    public function form( $instance )
    {
        $title = isset ( $instance['title'] ) ? $instance['title'] : '';
        $title = esc_attr( $title );

        printf(
            '<p><label for="%1$s">%2$s</label><br />
            <input type="text" name="%3$s" id="%1$s" value="%4$s" class="widefat"></p>',
            $this->get_field_id( 'title' ),
            'Title',
            $this->get_field_name( 'title' ),
            $title
        );

        $fields = isset ( $instance['fields'] ) ? $instance['fields'] : array();
        $field_num = count( $fields );
        $fields[ $field_num + 1 ] = '';
        $fields_html = array();
        $fields_counter = 0;

        foreach ( $fields as $name => $value )
        {
            $fields_html[] = sprintf(
                '<input type="text" name="%1$s[%2$s]" value="%3$s" class="widefat">',
                $this->get_field_name( 'fields' ),
                $fields_counter,
                esc_attr( $value )
            );
            $fields_counter += 1;
        }

        print 'Fields<br />' . join( '<br />', $fields_html );
    }

    /**
     * Renders the output.
     *
     * @see WP_Widget::widget()
     */
    public function widget( $args, $instance )
    {
        print $args['before_widget']
        . $args['before_title']
        . apply_filters( 'widget_title', $instance['title'] )
        . $args['after_title']
        . join( '<br />', $instance['fields'] )
        . $args['after_widget'];
    }

    /**
     * Prepares the content. Not.
     *
     * @param  array $new_instance New content
     * @param  array $old_instance Old content
     * @return array New content
     */
    public function update( $new_instance, $old_instance )
    {
        $instance          = $old_instance;
        $instance['title'] = esc_html( $new_instance['title'] );

        $instance['fields'] = array();

        if ( isset ( $new_instance['fields'] ) )
        {
            foreach ( $new_instance['fields'] as $value )
            {
                if ( '' !== trim( $value ) )
                    $instance['fields'][] = $value;
            }
        }

        return $instance;
    }

    /**
     * Tell WP we want to use this widget.
     *
     * @wp-hook widgets_init
     * @return void
     */
    public static function register()
    {
        register_widget( __CLASS__ );
    }
}

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