Why can't a user create or manage campaigns?
Even if a user is a System Adminstrator and has full access to the Campaign object, there is still an additional step needed if he/she will need the ability to create new campaigns or add members to it. Here is how to give a user full access to campaigns.
In Setup, select Manage Users > Users.
Find the user that should have access and click Edit link to the left of their name.
In the right hand column, check the box that says Marketing User.
Save the record.
The user should now see they have the ability to create new Campaigns.