Nope, a database can be created with hundreds of tables and no relationship between them.
Scenerio....I'm a DBA, call me lazy, call me unknowledgeable, whatever....I decide that I'm not going to let anyone create their own databases unless they require 10 or more tables. Otherwise, everyone will create their tables in MyOnlyDB. Makes it easier for me to administer it. Now 20 users each create one table for themselves. Is there a relationship required between the 20 tables? No.
While that's a REALLY far-off scenerio, it does show you aren't required to have relationships between tables in a database.
(BTW- I would NEVER do anything like that, it was just an example).
-SQLBill