To find infinite recursive loop in CTE

With Postgres it's quite easy to prevent this by collecting all visited nodes in an array.

Setup:

create table hierarchy (id integer, parent_id integer);

insert into hierarchy
values
(1, null), -- root element
(2, 1), -- first child
(3, 1), -- second child
(4, 3), 
(5, 4), 
(3, 5); -- endless loop

Recursive query:

with recursive tree as (
  select id, 
         parent_id, 
         array[id] as all_parents
  from hierarchy
  where parent_id is null
  
  union all
  
  select c.id, 
         c.parent_id,
         p.all_parents||c.id
  from hierarchy c
     join tree p
      on c.parent_id = p.id 
     and c.id <> ALL (p.all_parents) -- this is the trick to exclude the endless loops
)
select *
from tree;

---

To do this for multiple trees at the same time, you need to carry over the ID of the root node to the children:

with recursive tree as (
  select id, 
         parent_id, 
         array[id] as all_parents, 
         id as root_id
  from hierarchy
  where parent_id is null
  
  union all
  
  select c.id, 
         c.parent_id,
         p.all_parents||c.id, 
         p.root_id
  from hierarchy c
     join tree p
      on c.parent_id = p.id 
     and c.id <> ALL (p.all_parents) -- this is the trick to exclude the endless loops
     and c.root_id = p.root_id
)
select *
from tree;

Update for Postgres 14

Postgres 14 introduced the (standard compliant) CYCLE option to detect cycles:

with recursive tree as (
  select id, 
         parent_id
  from hierarchy
  where parent_id is null

  union all

  select c.id, 
         c.parent_id
  from hierarchy c
     join tree p
      on c.parent_id = p.id 
)
cycle id -- track cycles for this column
   set is_cycle -- adds a boolean column is_cycle
   using path -- adds a column that contains all parents for the id
select *
from tree
where not is_cycle

You haven't specified the dialect or your column names, so it is difficult to make the perfect example...

-- Some random data
IF OBJECT_ID('tempdb..#MyTable') IS NOT NULL
    DROP TABLE #MyTable

CREATE TABLE #MyTable (ID INT PRIMARY KEY, ParentID INT NULL, Description VARCHAR(100))
INSERT INTO #MyTable (ID, ParentID, Description) VALUES
(1, NULL, 'Parent'), -- Try changing the second value (NULL) to 1 or 2 or 3
(2, 1, 'Child'), -- Try changing the second value (1) to 2 
(3, 2, 'SubChild')
-- End random data

;WITH RecursiveCTE (StartingID, Level, Parents, Loop, ID, ParentID, Description) AS
(
    SELECT ID, 1, '|' + CAST(ID AS VARCHAR(MAX)) + '|', 0, * FROM #MyTable
    UNION ALL
    SELECT R.StartingID, R.Level + 1, 
        R.Parents + CAST(MT.ID AS VARCHAR(MAX)) + '|',
        CASE WHEN R.Parents LIKE '%|' + CAST(MT.ID AS VARCHAR(MAX)) + '|%' THEN 1 ELSE 0 END,
        MT.*
        FROM #MyTable MT
        INNER JOIN RecursiveCTE R ON R.ParentID = MT.ID AND R.Loop = 0
)

SELECT StartingID, Level, Parents, MAX(Loop) OVER (PARTITION BY StartingID) Loop, ID, ParentID, Description 
    FROM RecursiveCTE 
    ORDER BY StartingID, Level

Something like this will show if/where there are loops in the recursive cte. Look at the column Loop. With the data as is, there is no loops. In the comments there are examples on how to change the values to cause a loop.

In the end the recursive cte creates a VARCHAR(MAX) of ids in the form |id1|id2|id3| (called Parents) and then checks if the current ID is already in that "list". If yes, it sets the Loop column to 1. This column is checked in the recursive join (the ABD R.Loop = 0).

The ending query uses a MAX() OVER (PARTITION BY ...) to set to 1 the Loop column for a whole "block" of chains.

A little more complex, that generates a "better" report:

-- Some random data
IF OBJECT_ID('tempdb..#MyTable') IS NOT NULL
    DROP TABLE #MyTable

CREATE TABLE #MyTable (ID INT PRIMARY KEY, ParentID INT NULL, Description VARCHAR(100))
INSERT INTO #MyTable (ID, ParentID, Description) VALUES
(1, NULL, 'Parent'), -- Try changing the second value (NULL) to 1 or 2 or 3
(2, 1, 'Child'), -- Try changing the second value (1) to 2 
(3, 3, 'SubChild')
-- End random data

-- The "terminal" childrens (that are elements that don't have childrens
-- connected to them)
;WITH WithoutChildren AS
(
    SELECT MT1.* FROM #MyTable MT1
        WHERE NOT EXISTS (SELECT 1 FROM #MyTable MT2 WHERE MT1.ID != MT2.ID AND MT1.ID = MT2.ParentID)
)

, RecursiveCTE (StartingID, Level, Parents, Descriptions, Loop, ParentID) AS
(
    SELECT ID, -- StartingID 
        1, -- Level
        '|' + CAST(ID AS VARCHAR(MAX)) + '|', 
        '|' + CAST(Description AS VARCHAR(MAX)) + '|', 
        0, -- Loop
        ParentID
        FROM WithoutChildren
    UNION ALL
    SELECT R.StartingID, -- StartingID
        R.Level + 1, -- Level
        R.Parents + CAST(MT.ID AS VARCHAR(MAX)) + '|',
        R.Descriptions + CAST(MT.Description AS VARCHAR(MAX)) + '|', 
        CASE WHEN R.Parents LIKE '%|' + CAST(MT.ID AS VARCHAR(MAX)) + '|%' THEN 1 ELSE 0 END,
        MT.ParentID
        FROM #MyTable MT
        INNER JOIN RecursiveCTE R ON R.ParentID = MT.ID AND R.Loop = 0
)

SELECT * FROM RecursiveCTE 
    WHERE ParentID IS NULL OR Loop = 1

This query should return all the "last child" rows, with the full parent chain. The column Loop is 0 if there is no loop, 1 if there is a loop.