You need to UNION the results:
SELECT userID, SUM(Points) AS total
FROM
(
SELECT userID, SUM(amount1) AS "Points"
FROM [Company].[dbo].[Contest1]
WHERE userid NOT IN (0,1)
GROUP BY userId
UNION ALL
SELECT userId, SUM(amount2)/.65 AS "Category 2 Points"
FROM [Company].[dbo].[Contest2]
WHERE dateGiven >=201301 AND dateGiven <= 201305
GROUP BY userId
UNION ALL
SELECT userid, SUM(amount3) AS "Category 3 Points"
FROM [Company].[dbo].[Contest3]
WHERE userid NOT IN (1,2)
GROUP BY userid
) AS dt
GROUP BY userID
ORDER BY 2 DESC;
Edit: to get three seperate columns you simply use three SUMs instead of one:
SELECT userID, SUM("Category 1 Points"), SUM("Category 2 Points"), SUM("Category 3 Points")
FROM
(
SELECT userID, SUM(amount1) AS "Category 1 Points"
FROM [Company].[dbo].[Contest1]
WHERE userid NOT IN (0,1)
GROUP BY userId
UNION ALL
SELECT userId, SUM(amount2)/.65 AS "Category 2 Points"
FROM [Company].[dbo].[Contest2]
WHERE dateGiven >=201301 AND dateGiven <= 201305
GROUP BY userId
UNION ALL
SELECT userid, SUM(amount3) AS "Category 3 Points"
FROM [Company].[dbo].[Contest3]
WHERE userid NOT IN (1,2)
GROUP BY userid
) AS dt
GROUP BY userID
ORDER BY 2 DESC;
Of course there's only a single row per userDI/category so MIN or MAX would return the same result. This will return NULL for non-existing data, if you want 0 instead use COALESCE("Category x Points", 0).
You can also join the result sets, but unless it's guaranteed that each user particpated in each contest you need FULL OUTER JOINs using COALESCE:
SELECT userID, "Category 1 Points", "Category 2 Points", "Category 3 Points"
FROM
(
SELECT userID, SUM(amount1) AS "Category 1 Points"
FROM [Company].[dbo].[Contest1]
WHERE userid NOT IN (0,1)
GROUP BY userId
) AS t1
FULL JOIN
ON t1.userID = t2.userID
(
SELECT userId, SUM(amount2)/.65 AS "Category 2 Points"
FROM [Company].[dbo].[Contest2]
WHERE dateGiven >=201301 AND dateGiven <= 201305
GROUP BY userId
) AS t2
FULL JOIN
(
SELECT userid, SUM(amount3) AS "Category 3 Points"
FROM [Company].[dbo].[Contest3]
WHERE userid NOT IN (1,2)
GROUP BY userid
) AS t3
ON COALESCE(t1.userID, t2.userID) = t3.userID
ORDER BY 2 DESC;