If the semantics of your table require it, then add however many unique keys as you may need. For instance, if in your problem domain all "Employee" entities are uniquely identified by Name, then Name should have a unique index or constraint on it. If there can be two employees with the same name, then, of course, there should be no uniqueness constraint on that column.
I have a client now who needs to keep information per-school, per-fiscal year. They need a unique constraint (or index) on the school and year columns, combined. Sometimes these two are also the primary key, but even when they're not primary, they are unique.