MySQL subquery slows down drastically, but they work fine independently
In Query 3, you are basically executing a subquery for every row of mybigtable against itself.

To avoid this, you need to make two major changes:

MAJOR CHANGE #1 : Refactor the Query

Here is your original query

Select count(*) as total from mybigtable
where account_id=123 and email IN
(select distinct email from mybigtable where account_id=345)


You could try 

select count(*) EmailCount from
(
    select tbl123.email from
    (select email from mybigtable where account_id=123) tbl123
    INNER JOIN
    (select distinct email from mybigtable where account_id=345) tbl345
    using (email)
) A;


or maybe the count per email

select email,count(*) EmailCount from
(
    select tbl123.email from
    (select email from mybigtable where account_id=123) tbl123
    INNER JOIN
    (select distinct email from mybigtable where account_id=345) tbl345
    using (email)
) A group by email;


MAJOR CHANGE #2 : Proper Indexing

I think you have this already since Query 1 and Query 2 run fast. Make sure you have a compound index on (account_id,email). Do SHOW CREATE TABLE mybigtable\G and make sure you have one. If you don't have it or if you are not sure, then create the index anyway:

ALTER TABLE mybigtable ADD INDEX account_id_email_ndx (account_id,email);


UPDATE 2012-03-07 13:26 EST

If you want to do a NOT IN(), change the INNER JOIN to a LEFT JOIN and check for the right side being NULL, like this:

select count(*) EmailCount from
(
    select tbl123.email from
    (select email from mybigtable where account_id=123) tbl123
    LEFT JOIN
    (select distinct email from mybigtable where account_id=345) tbl345
    using (email)
    WHERE tbl345.email IS NULL
) A;


UPDATE 2012-03-07 14:13 EST

Please read these two links on doing JOINs


http://en.wikipedia.org/wiki/Sql_join
http://dev.mysql.com/doc/refman/5.5/en/join.html


Here is a great YouTube Video where I learned to refactor queries and the book it was based on


http://youtu.be/ZVisY-fEoMw
http://www.amazon.com/Refactoring-SQL-Applications-Stephane-Faroult/dp/B006TR0ZEO