Salesforce.com has put some silly restrictions and one of those is limit on No. of Unique fields per object. It allows only 3 External ID fields per object and considers Unique fields as type of external Id’s only.So, you can create maximum 3 Unique fields per object but can get this limit extended by requesting the salesforce via raising a Case.

ADM 201 Question:- Only 3 External ID Fields can be created on an Object.
ADM 201 Question:- Only Text, Email, Number fields can be made External Id fields.

Note:- You can not make a field unique if it contains data which is not unique.