I can get a list of unique constraints fairly easily with the following query:
select * from INFORMATION_SCHEMA.TABLE_CONSTRAINTS where CONSTRAINT_TYPE=\'UNIQUE\
Ed is correct, the columns are exposed on the constraint column usage view, here is the SQL for it.
select TC.Constraint_Name, CC.Column_Name from information_schema.table_constraints TC
inner join information_schema.constraint_column_usage CC on TC.Constraint_Name = CC.Constraint_Name
where TC.constraint_type = 'Unique'
order by TC.Constraint_Name