Stick,
as usual Dagon has the right of it. I would however add a couple of points to the above.
You should never create a unique index to enforce a unique constraint because it is not self-evident that the DBA really meant a unique constraint. Uniqueness should always be achieved by creating a constraint, so that the intent is obvious.
If the db automatically creates an index "behind the scenes" well and good. However, if a suitable index already exists, oracle will automatically use it, without creating another. Coercing the creation of an unnecessary unique index is a waste of time and effort.
If you have a unique constraint on a column, then it may be used in referential integrity constraints (i.e. foreign keys). You can't create a foreign key to an index.
If in the future Oracle corporation decided to use some means other than indexes to enforce uniqueness, then a unique constraint would continue to work, whereas an index might not. This is incredibly unlikely, but it is (IMHO) a good practice to go with what the manufacturer intended, rather than try to cajole a system into doing something 'clever'.
Regards
T
Grinding away at things Oracular