It is possible to set one-to-many associations between standard objects (as described here), however that does not extend to custom objects. Currently it is only possible to create many-to-many relationships, which significantly reduces the usability and functionality of custom objects.
As an example, we have added a custom object called Partner Agreements. We would like to associate that object to one company we share the agreement with, but a company should only be allowed to have one of these associations.