query "not equal" doesn't work

SELECT * FROM all_conversations WHERE deleted_1 <> 1 OR deleted_1 IS NULL

NULL values need special treatment: http://dev.mysql.com/doc/refman/5.1/en/working-with-null.html

I'd suggest using the diamond operator (<>) in favor of != as the first one is valid SQL and the second one is a MySQL addition.

I recommend to use NULL-safe operator and negation

SELECT * FROM `all_conversations` WHERE NOT(`deleted_1` <=> '1');

Can you try this: deleted_1 is not null and deleted_1 != '1'?

mysql> select 0 is not null and 0 != '1', 1 is not null and 1 != '1', null is not null and null != '1';
+----------------------------+----------------------------+----------------------------------+
| 0 is not null and 0 != '1' | 1 is not null and 1 != '1' | null is not null and null != '1' |
+----------------------------+----------------------------+----------------------------------+
|                          1 |                          0 |                                0 |
+----------------------------+----------------------------+----------------------------------+

Or this deleted_1 is null or deleted_1 != '1':

mysql> select 0 is null or 0 != '1', 1 is null or 1 != '1', null is null or null != '1';
+-----------------------+-----------------------+-----------------------------+
| 0 is null or 0 != '1' | 1 is null or 1 != '1' | null is null or null != '1' |
+-----------------------+-----------------------+-----------------------------+
|                     1 |                     0 |                           1 |
+-----------------------+-----------------------+-----------------------------+

It really depends on what you wanna get back.