Select products where the category belongs to any category in the hierarchy

Computers
    Processors
        Intel
            Pentium
            Core 2 Duo
        AMD
            Athlon

SELECT * FROM products
   INNER JOIN categories ON categories.id = products.category_id
WHERE categories.lft > 2 and categories.rgt < 11

with catCTE (catid, parentid)
as
(
select cat.catid, cat.catparentid from cat where cat.name = 'Processors'
UNION ALL
select cat.catid, cat.catparentid from cat inner join catCTE on cat.catparentid=catcte.catid
)
select distinct * from catCTE

categoriesSet = empty set
while new.size > 0:
  new = select * from categories where parent in categoriesSet
  categoriesSet = categoriesSet+new

select *
from products
where products.category_id IN
  (select c2.category_id
   from categories c1 inner join categories c2 on c1.category_id = c2.parent_id
   where c1.category = 'Processors'
   group by c2.category_id)

CREATE TABLE #categories (id INT NOT NULL, parentId INT, [name] NVARCHAR(100))
INSERT INTO #categories
    SELECT 1, NULL, 'Computers'
    UNION
SELECT 2, 1, 'Processors'
    UNION
SELECT 3, 2, 'Intel'
    UNION
SELECT 4, 2, 'AMD'
    UNION
SELECT 5, 3, 'Pentium'
    UNION
SELECT 6, 3, 'Core 2 Duo'
    UNION
SELECT 7, 4, 'Athlon'
SELECT *
    FROM #categories
DECLARE @id INT
    SET @id = 2
            ; WITH r(id, parentid, [name]) AS (
    SELECT id, parentid, [name]
        FROM #categories c
        WHERE id = @id
        UNION ALL
    SELECT c.id, c.parentid, c.[name]
        FROM #categories c  JOIN r ON c.parentid=r.id
    )
SELECT *
    FROM products
    WHERE p.productd IN
(SELECT id
    FROM r)
DROP TABLE #categories

DECLARE @startingCatagoryId int
DECLARE @current int
SET @startingCatagoryId = 13813 -- or whatever the CatagoryId is for 'Processors'

CREATE TABLE #CatagoriesToFindChildrenFor
(CatagoryId int)

CREATE TABLE #CatagoryTree
(CatagoryId int)

INSERT INTO #CatagoriesToFindChildrenFor VALUES (@startingCatagoryId)

WHILE (SELECT count(*) FROM #CatagoriesToFindChildrenFor) > 0
BEGIN
    SET @current = (SELECT TOP 1 * FROM #CatagoriesToFindChildrenFor)

    INSERT INTO #CatagoriesToFindChildrenFor
    SELECT ID FROM Catagory WHERE ParentCatagoryId = @current AND Deleted = 0

    INSERT INTO #CatagoryTree VALUES (@current)
    DELETE #CatagoriesToFindChildrenFor WHERE CatagoryId = @current
END

SELECT * FROM #CatagoryTree ORDER BY CatagoryId

DROP TABLE #CatagoriesToFindChildrenFor
DROP TABLE #CatagoryTree

-- create a categories table and fill it with 10 rows (with random parentIds)
CREATE TABLE Categories ( Id uniqueidentifier, ParentId uniqueidentifier )
GO

INSERT
INTO   Categories
SELECT NEWID(),
       NULL
GO

INSERT
INTO   Categories
SELECT   TOP(1)NEWID(),
         Id
FROM     Categories
ORDER BY Id
GO 9


DECLARE  @lvl INT,            -- holds onto the level as we move throught the hierarchy
         @Id Uniqueidentifier -- the id of the current item in the stack

SET @lvl = 1

CREATE TABLE #stack (item UNIQUEIDENTIFIER, [lvl] INT)
-- we fill fill this table with the ids we want
CREATE TABLE #tmpCategories (Id UNIQUEIDENTIFIER)

-- for this example we’ll just select all the ids
-- if we want all the children of a specific parent we would include it’s id in
-- this where clause
INSERT INTO #stack SELECT Id, @lvl FROM Categories WHERE ParentId IS NULL

WHILE @lvl > 0
BEGIN -- begin 1

      IF EXISTS ( SELECT * FROM #stack WHERE lvl = @lvl )
      BEGIN -- begin 2

      SELECT @Id = [item]
      FROM #stack
      WHERE lvl = @lvl

      INSERT INTO #tmpCategories
      SELECT @Id

      DELETE FROM #stack
      WHERE lvl = @lvl
      AND item = @Id

      INSERT INTO #stack
      SELECT Id, @lvl + 1
      FROM   Categories
      WHERE  ParentId = @Id

      IF @@ROWCOUNT > 0
      BEGIN -- begin 3
         SELECT @lvl = @lvl + 1
      END -- end 3
   END -- end 2
   ELSE
   SELECT @lvl = @lvl - 1

END -- end 1

DROP TABLE #stack

SELECT * FROM #tmpCategories
DROP TABLE #tmpCategories
DROP TABLE Categories