Standard sql:

    select key, value, asof
    from (
      select *, row_number() over (partition by key order by asof desc) as rn
      from <table>
    ) t
    where rn = 1

postgresql:

    select distinct on (key)
    key, value, asof
    from <table>
    order by key, asof desc

The DISTINCT ON clause takes the first row that the query returns, which the ORDER BY makes sure is the latest value

Disclaimer: I've used both methods, but haven't tested the perf against each other or the self-join.