Only one primary key is allowed on a table but multiple unique indexes can be added up to the maximum allowed number of indexes for the table (SQL Server = 250 (1 x clustered, 249 x non clustered) and SQL 2008 and SQL 2012 = 1000 (1 x clustered, 999 x non clustered)).
Primary keys cannot contain nullable columns but unique indexes can. Note, that only one NULL is allowed. If the index is created across multiple columns, each combination of values and NULL’s must be unique.
By default, unless you specify otherwise in the create statement and providing that a clustered index does not already exists, the primary key is created as a clustered index. Unique indexes however are created by default as non clustered indexes unless you specify otherwise and providing that a clustered index does not already exist.