A count() displays the number of rows found for your group. Since you're grouping on estate, it will count the number of rows you join to estate. Joins will multiply the number of rows, so 3 x 10 = 30 sounds like the correct count. Run the query without GROUP BY to see what's happening.
One way to fix it would look like this:
SELECT
e.name as estate_name,
g.name as governing_body,
(select count(*) from stands s where s.estate_id = e.id) as stands,
(select count(*) from services sp where sp.estate_id = e.id) as services
FROM estates e
LEFT JOIN governing_bodies g on e.governing_body_id = g.id
Writing out Alex Martelli's informative answer:
SELECT
e.name as estate_name
, g.name as governing_body
, count(distinct s.id) as total_stands
, count(distinct sp.id) as service_providers
FROM estates e
LEFT JOIN governing_bodies
ON e.governing_body_id = g.id
LEFT JOIN stands s
ON s.estate_id = e.id
LEFT JOIN services sp
ON sp.estate_id = e.id
GROUP BY e.id, g.name
Or, as a more complex alternative with JOIN syntax:
SELECT
e.name as estate_name,
g.name as governing_body,
IsNull(stand_count.total,0) as stand_count,
IsNull(service_count.total,0) as service_count
FROM estates e
LEFT JOIN governing_bodies g on e.governing_body_id = g.id
LEFT JOIN (
select estate_id, total = count(*) from stands group by estate_id
) stand_count on stand_count.estate_id = e.id
LEFT JOIN (
select estate_id, total = count(*) from services group by estate_id
) service_count on service_count.estate_id = e.id
GROUP BY
e.name,
g.name,
IsNull(stand_count.total,0),
IsNull(service_count.total,0)