PostgreSQL aggregate or window function to return just the last value

I'm using an aggregate function with the OVER clause in PostgreSQL 9.1 and I want to return just the last row for each window. The last_value() window function sounds like it might do what I want - but it doesn't. It returns a row for each row in the window, whereas I want just one row per window

A simplified example:

SELECT a, some_func_like_last_value(b) OVER (PARTITION BY a ORDER BY b)
FROM
(
    SELECT 1 AS a, 'do not want this' AS b
    UNION SELECT 1, 'just want this'
) sub

I want this to return one row:

1, 'just want this'