Simplest way to do a recursive self-join?

Using CTEs you can do it this way

DECLARE @Table TABLE(
        PersonID INT,
        Initials VARCHAR(20),
        ParentID INT
)

INSERT INTO @Table SELECT     1,'CJ',NULL
INSERT INTO @Table SELECT     2,'EB',1
INSERT INTO @Table SELECT     3,'MB',1
INSERT INTO @Table SELECT     4,'SW',2
INSERT INTO @Table SELECT     5,'YT',NULL
INSERT INTO @Table SELECT     6,'IS',5

DECLARE @PersonID INT

SELECT @PersonID = 1

;WITH Selects AS (
        SELECT *
        FROM    @Table
        WHERE   PersonID = @PersonID
        UNION ALL
        SELECT  t.*
        FROM    @Table t INNER JOIN
                Selects s ON t.ParentID = s.PersonID
)
SELECT  *
FROm    Selects

WITH    q AS 
        (
        SELECT  *
        FROM    mytable
        WHERE   ParentID IS NULL -- this condition defines the ultimate ancestors in your chain, change it as appropriate
        UNION ALL
        SELECT  m.*
        FROM    mytable m
        JOIN    q
        ON      m.parentID = q.PersonID
        )
SELECT  *
FROM    q

By adding the ordering condition, you can preserve the tree order:

WITH    q AS 
        (
        SELECT  m.*, CAST(ROW_NUMBER() OVER (ORDER BY m.PersonId) AS VARCHAR(MAX)) COLLATE Latin1_General_BIN AS bc
        FROM    mytable m
        WHERE   ParentID IS NULL
        UNION ALL
        SELECT  m.*,  q.bc + '.' + CAST(ROW_NUMBER() OVER (PARTITION BY m.ParentID ORDER BY m.PersonID) AS VARCHAR(MAX)) COLLATE Latin1_General_BIN
        FROM    mytable m
        JOIN    q
        ON      m.parentID = q.PersonID
        )
SELECT  *
FROM    q
ORDER BY
        bc

By changing the ORDER BY condition you can change the ordering of the siblings.

The Quassnoi query with a change for large table. Parents with more childs then 10: Formating as str(5) the row_number()

WITH    q AS 
        (
        SELECT  m.*, CAST(str(ROW_NUMBER() OVER (ORDER BY m.ordernum),5) AS VARCHAR(MAX)) COLLATE Latin1_General_BIN AS bc
        FROM    #t m
        WHERE   ParentID =0
        UNION ALL
        SELECT  m.*,  q.bc + '.' + str(ROW_NUMBER()  OVER (PARTITION BY m.ParentID ORDER BY m.ordernum),5) COLLATE Latin1_General_BIN
        FROM    #t m
        JOIN    q
        ON      m.parentID = q.DBID
        )
SELECT  *
FROM    q
ORDER BY
        bc