When a table is normalized, the non-key columns depend on the key used.
From a relational model point of view, it is standard to have tables that are in Third Normal Form. Normalized physical design provides the greatest ease of maintenance, and databases in this form are clearly understood by developers.
However, a fully normalized design may not always yield the best performance. Sybase recommends that you design databases for Third Normal Form, however, if performance issues arise, you may have to denormalize to solve them.