It is ugly and performs badly, but technically this works on any table with at least one unique field AND works in SQL 2000.
SELECT (SELECT COUNT(*) FROM myTable T1 WHERE T1.UniqueField<=T2.UniqueField) as RowNum, T2.OtherField
FROM myTable T2
ORDER By T2.UniqueField
Note: If you use this approach and add a WHERE clause to the outer SELECT, you have to added it to the inner SELECT also if you want the numbers to be continuous.