I agree with Peter on PK requirements on OLTP tables.
However, non-OLTP tables (2nd hand data) generally do not require Primary Key and 3NF design. Example: audit, logging, history, reporting and staging tables.
While Primary Key requires a unique constraint, it does not have to be a clustered index. It can be an NC index.
If you are defining a table like:
create table Celebrity (
CelebrityID int identity(1,1) primary key,
Name varchar(64) )
SQL Server automatically creates a clustered index on CelebrityID.
I can define a second index on CelebrityID:
CREATE UNIQUE NONCLUSTERED INDEX [idxCelebrityUnique] ON [dbo].[Celebrity]
and remove the clustered index, and place it on a different column(s).
Kalman Toth, SQL Server 2008 Training