SELECT user_event_id, event_title
from user_events
where user_id = 63
order by user_event_id desc
limit 1
Most DBMS does not allow to include event_title into field list (like author did) because it is not used for grouping and not aggregate function. But mysql does, often with unexpected result.
UPDATE:
This query returns only one record if there are several records with the same min user_event_id for the user. So it addresses slightly different problem, than solution of Barry Brown - which return all records with equal user_event_id.