Try changing your date format to the standard ISO 8601 format:
INSERT INTO envios (fecha_estimada_entrega)
VALUES (ADDDATE('2011-10-15', INTERVAL 8 DAY));
MySQL is probably trying to parse 15 as a month number, failing, and converting your '15/10/2011' date to NULL. Switching to ISO 8601 (the one true date format BTW) gets me sensible results:
mysql> select ADDDATE('2011-10-15', INTERVAL 8 DAY);
+---------------------------------------+
| ADDDATE('2011-10-15', INTERVAL 8 DAY) |
+---------------------------------------+
| 2011-10-23 |
+---------------------------------------+
As an aside, you should always use ISO 8601 date and time formats internally and limit other formats to the edges (i.e. user input and final display). You'll save yourself a lot of trouble that way and they'll even sort properly as strings.