Database Users and Permissions

I have tried this question twice before, but with no success. Maybe
I'm asking the wrong question, or maybe I'm asking the question
wrongly. I'm hoping it was the latter, and trying to rephrase.

If you have a number of databases (on the same machine) and a number
of users. Some users must connect to some databases, and others must
connect to other databases. What is the smartest way of managing this?
As I see it, I can't give a user group access to a database, or even a
user. I can only give the user/group access on tabel level, not at
database level. How do you guys do it?

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Med venlig hilsen/Best regards,
Søren Neigaard mailto:neigaard(at)e-box(dot)dk
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"Beware of bugs in the above code; I have only proved it correct, not tried it."