Oracle: how to UPSERT (update or insert into a table?)

The UPSERT operation either updates or inserts a row in a table, depending if the table already has a row that matches the data:

if table t has a row exists that has key X:
    update t set mystuff... where mykey=X
else
    insert into t mystuff...

Since Oracle doesn’t have a specific UPSERT statement, what’s the best way to do this?