If you are doing a comparison, you should not be converting the date to a string. You should be comparing to another date. Otherwise, Oracle won't be able to use a non function-based index on the date column.
In general, that is, you're much better off coding
WHERE some_indexed_date_column = to_date( :string_bind_variable,
<<format mask>> )
rather than
WHERE to_char( some_indexed_date_column,
<<format mask>> ) = :string_bind_variable
Of course, if your bind variable can be a DATE rather than a VARCHAR2, that's even better because then you don't have to do any data type conversion and the optimizer has a much easier time of estimating cardinalities.
If you are trying to do some manipulation of the date-- for example, if you want to compare the day portion while omitting the time portion of the date-- you may want to use function-based indexes. For example, if you wanted to find all the rows that were created some time today
WHERE trunc( some_date_column ) = date '2011-11-04'
you could either create a function-based index on the date column
CREATE INDEX idx_trunc_dt
ON table_name( trunc( some_date_column ) )
or you could rewrite the query to do something like
WHERE some_date_column >= date '2011-11-04'
AND some_date_column < date '2011-11-05'