This is probably fastest:
SELECT u.*
FROM usr u -- avoiding "User" as table name
JOIN LATERAL (
SELECT name
FROM userevent
WHERE user_id = u.id
ORDER BY date DESC NULLS LAST
LIMIT 1
) ue ON ue.name = 'played';
LATERAL requires Postgres 9.3+:
Or you could use DISTINCT ON (faster for few rows per user):
SELECT u.*
FROM usr u -- avoiding "User" as table name
JOIN (
SELECT DISTINCT ON (user_id)
user_id, name
FROM userevent
ORDER BY user_id, date DESC NULLS LAST
) ue ON ue.user_id = u.id
AND ue.name = 'played';
Details for DISTINCT ON:
SQL Fiddle with valid test case.
If date is defined NOT NULL, you don't need NULLS LAST. (Neither in the index below.)
Key to read performance for both but especially the first query is a matching multicolumn index:
CREATE INDEX userevent_foo_idx ON userevent (user_id, date DESC NULLS LAST, name);
Aside: Never use reserved words as identifiers.