I assume you are on 2005 or better? If so, look into the OUTPUT clause, you shouldn't need row-level triggers. For example:
USE tempdb;
GO
CREATE TABLE t1 (foo int);
CREATE TABLE t2 (id int IDENTITY, foo int);
CREATE TABLE t3 (t2_id int);
GO
CREATE TRIGGER t1_insert ON t1
FOR INSERT AS
BEGIN
DECLARE @new_rows TABLE(new_id INT, old_foo INT);
INSERT t2(foo)
OUTPUT inserted.id, inserted.foo
INTO @new_rows
SELECT foo
FROM inserted;
INSERT t3 SELECT new_id FROM @new_rows;
END
GO
INSERT t1(foo) SELECT 1 UNION ALL SELECT 5;
SELECT * FROM t1;
SELECT * FROM t2;
SELECT * FROM t3;
GO
DROP TABLE t1,t2,t3;
You could also manage this by having a trigger on T1 that inserts into T2, then a trigger on T2 that inserts into T3. This isn't going to be as efficient IMHO, and is not easier to manage, but I will submit that it is easier to follow (and may be your only option if you are stuck on 2000). Both could be set-based and wouldn't need cursors or any other row-by-row processing method.
USE tempdb;
GO
CREATE TABLE t1 (foo int);
CREATE TABLE t2 (id int IDENTITY, foo int);
CREATE TABLE t3 (t2_id int);
GO
CREATE TRIGGER t1_insert ON t1
FOR INSERT AS
BEGIN
INSERT t2(foo)
SELECT foo FROM inserted;
END
GO
CREATE TRIGGER t2_insert ON t2
FOR INSERT AS
BEGIN
INSERT t3(t2_id)
SELECT id FROM inserted;
END
GO
INSERT t1(foo) SELECT 1 UNION ALL SELECT 5;
SELECT * FROM t1;
SELECT * FROM t2;
SELECT * FROM t3;
GO
DROP TABLE t1,t2,t3;
(BTW, if you are going for identity values, use SCOPE_IDENTITY(), not @@IDENTITY.)