Relational Database Design Patterns?
There's a book in Martin Fowler's Signature Series called Refactoring Databases. That provides a list of techniques for refactoring databases. I can't say I've heard a list of database patterns so much.
I would also highly recommend David C. Hay's Data Model Patterns and the follow up A Metadata Map which builds on the first and is far more ambitious and intriguing. The Preface alone is enlightening.
Also a great place to look for some pre-canned database models is Len Silverston's Data Model Resource Book Series Volume 1 contains universally applicable data models (employees, accounts, shipping, purchases, etc), Volume 2 contains industry specific data models (accounting, healthcare, etc), Volume 3 provides data model patterns.
Finally, while this book is ostensibly about UML and Object Modelling, Peter Coad's Modeling in Color With UML provides an "archetype" driven process of entity modeling starting from the premise that there are 4 core archetypes of any object/data model
Design patterns aren't trivially reusable solutions.
Design patterns are reusable, by definition. They're patterns you detect in other good solutions.
A pattern is not trivially reusable. You can implement your down design following the pattern however.
Relational design patterns include things like:
One-to-Many relationships (master-detail, parent-child) relationships using a foreign key.
Many-to-Many relationships with a bridge table.
Optional one-to-one relationships managed with NULLs in the FK column.
Star-Schema: Dimension and Fact, OLAP design.
Fully normalized OLTP design.
Multiple indexed search columns in a dimension.
"Lookup table" that contains PK, description and code value(s) used by one or more applications. Why have code? I don't know, but when they have to be used, this is a way to manage the codes.
Uni-table. [Some call this an anti-pattern; it's a pattern, sometimes it's bad, sometimes it's good.] This is a table with lots of pre-joined stuff that violates second and third normal form.
Array table. This is a table that violates first normal form by having an array or sequence of values in the columns.
Mixed-use database. This is a database normalized for transaction processing but with lots of extra indexes for reporting and analysis. It's an anti-pattern -- don't do this. People do it anyway, so it's still a pattern.
Most folks who design databases can easily rattle off a half-dozen "It's another one of those"; these are design patterns that they use on a regular basis.
And this doesn't include administrative and operational patterns of use and management.