When you have a project which still runs on WordPress 3.3 (Oh boy..) and want to use the $wpdb::delete() method you can easily extend the wpdb class by dropping this db.php file into WP_CONTENT_DIR. Thanks @toscho for the hint.

db.php

<?php
/**
 * This class provides the $wpdb::delete() method which was introduced in WordPress 3.4.
 *
 * @link https://core.trac.wordpress.org/ticket/18948
 */
class DS_wpdb extends wpdb {

	/**
	 * Delete a row in the table
	 *
	 * <code>
	 * wpdb::delete( 'table', array( 'ID' => 1 ) )
	 * wpdb::delete( 'table', array( 'ID' => 1 ), array( '%d' ) )
	 * </code>
	 *
	 * @since 3.4.0
	 * @see wpdb::prepare()
	 * @see wpdb::$field_types
	 * @see wp_set_wpdb_vars()
	 *
	 * @param string $table table name
	 * @param array $where A named array of WHERE clauses (in column => value pairs). Multiple clauses will be joined with ANDs. Both $where columns and $where values should be "raw".
	 * @param array|string $where_format Optional. An array of formats to be mapped to each of the values in $where. If string, that format will be used for all of the items in $where. A format is one of '%d', '%f', '%s' (integer, float, string). If omitted, all values in $where will be treated as strings unless otherwise specified in wpdb::$field_types.
	 * @return int|false The number of rows updated, or false on error.
	 */
	function delete( $table, $where, $where_format = null ) {
		if ( ! is_array( $where ) )
			return false;

		$bits = $wheres = array();

		$where_formats = $where_format = (array) $where_format;

		foreach ( array_keys( $where ) as $field ) {
			if ( !empty( $where_format ) ) {
				$form = ( $form = array_shift( $where_formats ) ) ? $form : $where_format[0];
			} elseif ( isset( $this->field_types[ $field ] ) ) {
				$form = $this->field_types[ $field ];
			} else {
				$form = '%s';
			}

			$wheres[] = "$field = $form";
		}

		$sql = "DELETE FROM $table WHERE " . implode( ' AND ', $wheres );
		return $this->query( $this->prepare( $sql, $where ) );
	}
}

$wpdb = new DS_wpdb( DB_USER, DB_PASSWORD, DB_NAME, DB_HOST );