A Primary Key is really just a candidate key that does not allow for NULL. As such, in SQL terms - it's no different than any other unique key.
However, for our non-theoretical RDBMS's, you should have a Primary Key - I've never heard it argued otherwise. If that Primary Key is a surrogate key, then you should also have unique constraints on the natural key(s).
The important bit to walk away with is that you should have unique constraints on all the candidate (whether natural or surrogate) keys. You should then pick the one that is easiest to reference in a Foreign Key to be your Primary Key*.
You should also have a clustered index*. this could be your Primary Key, or a natural key - but it's not required to be either. You should pick your clustered index based on query usage of the table. When in doubt, the Primary Key is not a bad first choice.
Though it's technically only required to refer to a unique key in a foreign key relationship, it's accepted standard practice to greatly favor the primary key. In fact, I wouldn't be surprised if some RDBMS only allow primary key references.
Edit: It's been pointed out that Oracle's term of "clustered table" and "clustered index" are different than Sql Server. The equivalent of what I'm speaking of in Oracle-ese is an Index Ordered Table and it is recommended for OLTP tables - which, I think, would be the main focus of SO questions. I assume if you're responsible for a large OLAP data warehouse, you should already have your own opinions on database design and optimization.
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