UNION'd queries should produce the same columns (name, type). Set unused columns to NULL or use a differenciation column:
SELECT
SUM(count) as `total`,
'today' as `when`
FROM
statistics
WHERE
name = "test"
AND $P{oneDayAgo} <= datetime
AND datetime <= $P{now}
UNION
SELECT
SUM(count) as `total`,
'thisWeek' as `when`
FROM
statistics
WHERE
name = "test"
AND $P{oneWeekAgo} <= datetime
AND datetime <= $P{now}
UNION
SELECT
SUM(count) as `total`,
'thisMonth' as `when`
FROM
statistics
WHERE
name = "test"
AND $P{oneMonthAgo} <= datetime
AND datetime <= $P{now}
streetpc
2009-06-16 16:41:10