Returning a ResultSet

You should never pass a ResultSet around through public methods. This is prone to resource leaking because you’re forced to keep the statement and the connection open. Closing them would implicitly close the result set. But keeping them open would cause them to dangle around and cause the DB to run out of resources when there are too many of them open.

Map it to a collection of Javabeans like so and return it instead:

public List<Biler> list() throws SQLException {
    Connection connection = null;
    PreparedStatement statement = null;
    ResultSet resultSet = null;
    List<Biler> bilers = new ArrayList<Biler>();

    try {
        connection = database.getConnection();
        statement = connection.prepareStatement("SELECT id, name, value FROM Biler");
        resultSet = statement.executeQuery();

        while (resultSet.next()) {
            Biler biler = new Biler();
            biler.setId(resultSet.getLong("id"));
            biler.setName(resultSet.getString("name"));
            biler.setValue(resultSet.getInt("value"));
            bilers.add(biler);
        }
    } finally {
        if (resultSet != null) try { resultSet.close(); } catch (SQLException ignore) {}
        if (statement != null) try { statement.close(); } catch (SQLException ignore) {}
        if (connection != null) try { connection.close(); } catch (SQLException ignore) {}
    }

    return bilers;
}

Or, if you’re on Java 7 already, just make use of try-with-resources statement which will auto-close those resources:

public List<Biler> list() throws SQLException {
    List<Biler> bilers = new ArrayList<Biler>();

    try (
        Connection connection = database.getConnection();
        PreparedStatement statement = connection.prepareStatement("SELECT id, name, value FROM Biler");
        ResultSet resultSet = statement.executeQuery();
    ) {
        while (resultSet.next()) {
            Biler biler = new Biler();
            biler.setId(resultSet.getLong("id"));
            biler.setName(resultSet.getString("name"));
            biler.setValue(resultSet.getInt("value"));
            bilers.add(biler);
        }
    }

    return bilers;
}

By the way, you should not be declaring the Connection, Statement and ResultSet as instance variables at all (major threadsafety problem!), nor be swallowing the SQLException at that point at all (the caller will have no clue that a problem occurred), nor be closing the resources in the same try (if e.g. result set close throws an exception, then statement and connection are still open). All those issues are fixed in the above code snippets.