Your problem is that the short version of dates uses midnight as the default. So your query is actually:
SELECT users.* FROM users
WHERE created_at >= '2011-12-01 00:00:00'
AND created_at <= '2011-12-06 00:00:00'
This is why you aren't seeing the record for 10:45.
Change it to:
SELECT users.* FROM users
WHERE created_at >= '2011-12-01'
AND created_at <= '2011-12-07'
You can also use:
SELECT users.* from users
WHERE created_at >= '2011-12-01'
AND created_at <= date_add('2011-12-01', INTERVAL 7 DAY)
Which will select all users in the same interval you are looking for.
You might also find the BETWEEN operator more readable:
SELECT users.* from users
WHERE created_at BETWEEN('2011-12-01', date_add('2011-12-01', INTERVAL 7 DAY));