I plan to open a roth IRA stock account under both my wife and I. It is much easier to manage only one account.

Is this allowed? Could we put in totally $6000 for year 2002? What is the difference if each of us open a roth IRA account?

Thanks.

The I in IRA stands for Individual. You can not open a "family" IRA because they don't exist. So if you wish to contribute $6000 to a Roth "as a family" you must do it in an separate account for each of you of $3000.
Reminds me of that old saying "The family that saves together......" or am I in the wrong Church?

Actually, the "I" in IRA stands for Ira. The retirement vehicle was named IRA after Ira Cohen, who was an actuary at the IRS who was one of the principal drafters of ERISA.