Левое соединение должно делать вашу работу.
SELECT event.`eventid`,
event.`name`,
`eventtime`,
`location`,
`datecreated`,
`dateofevent`,
`categoryname`,
`description`,
Count(participantlogs.eventid)
FROM event,
recreationalcategory,
participantlogs
WHERE (recreationalcategory.categoryid = event.categoryid OR recreationalcategory.categoryid is null)
AND participantlogs.eventid = event.eventid
GROUP BY event.eventid
просто используйте left join
SELECT event.`eventid`,
event.`name`,
`eventtime`,
`location`,
`datecreated`,
`dateofevent`,
`categoryname`,
`description`,
Count(participantlogs.eventid)
FROM event
left join recreationalcategory
on recreationalcategory.categoryid = event.categoryid
join participantlo on
on participantlogs.eventid = event.eventid
GROUP BY event.eventid