It is inclusive. You are comparing datetimes to dates. The second date is interpreted as midnight when the day starts.
One way to fix this is:
SELECT *
FROM Cases
WHERE cast(created_at as date) BETWEEN '2013-05-01' AND '2013-05-01'
Another way to fix it is with explicit binary comparisons
SELECT *
FROM Cases
WHERE created_at >= '2013-05-01' AND created_at < '2013-05-02'
Aaron Bertrand has a long blog entry on dates (here), where he discusses this and other date issues.