How are you running the website? Are you using Sitefinity's Project Manager or Visual Studio. In these 2 scenarios, it's rare to receive this error. If you do get the error in these scenarios, then it can normally be fixed like this:
On the other hand, if you're running the website using IIS then you probably also choose to use a local-attached database during Sitefinity's initial setup instead of providing a database hostname/username/password. Local attached databases create a user instance for the database. IIS, by default, runs as a special user and this user doesn't have these permissions.
I've never discovered an easy way to fix this. Instead, when using IIS, I explicitly provide a hostname (localhost\sqlexpress) and a database username & password.
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