If your code does not close ResultSets or PreparedStatements when done using then, your application will hog scarce resources — like cursors — in the database. See, for example:

• ResultSet not closed when connection closed?
• What happens to the original resultSet when it is returned from a method into a new object?

The garbage collector does not know anything about closing ResultSets or PreparedStatements, so GC won't automagically take care of that for you. What will? Java 7's try-with-resources statement!