The query below lists all unique indexes in the database.
Check out also list of unique constraints.
select i.[name] as index_name, substring(column_names, 1, len(column_names)-1) as [columns], case when i.[type] = 1 then 'Clustered unique index' when i.type = 2 then 'Unique index' end as index_type, schema_name(t.schema_id) + '.' + t.[name] as table_view, case when t.[type] = 'U' then 'Table' when t.[type] = 'V' then 'View' end as [object_type], case when c.[type] = 'PK' then 'Primary key' when c.[type] = 'UQ' then 'Unique constraint' end as constraint_type, c.[name] as constraint_name from sys.objects as t left outer join sys.indexes as i on t.object_id = i.object_id left outer join sys.key_constraints as c on i.object_id = c.parent_object_id and i.index_id = c.unique_index_id cross apply (select col.[name] + ', ' from sys.index_columns as ic inner join sys.columns as col on ic.object_id = col.object_id and ic.column_id = col.column_id where ic.object_id = t.object_id and ic.index_id = i.index_id order by col.column_id for xml path ('') ) as D (column_names) where is_unique = 1 and t.is_ms_shipped <> 1 order by i.[name]
Unique indexes in the AdventureWorksLT database: