Would it be a good idea if you had one account which would require two different passwords ?

For example your login details were:

email: example@gmail.com
password 1: P4$$w0rd1
password 2: HereIsMySecondPassword


Now when the user logs in to my site he is required to enter both passwords.
Would this be a better idea than just one stronger password ? The user could choose two passwords which he can easier remember than one strong.

Not really. It's essentially one password, with a press of the return key as one character.

It adds complexity to the log in process, which isn't generally a good thing (users would probably choose one good password, and one quick to type password). Don't forget @AviD's rule: "Security at the expense of usability, comes at the expense of security"

Depending on how the passwords were stored, they would slightly decrease the ability of attackers to brute force accounts, since an attacker would need to break both parts. I doubt that this balances out the usability issue though.
