Depends on which version of OS X you are running. When OS X first appeared it had a way of booting in Classic which would run OS 9 programmes. If you have a new machine with OS X (10.4) then your old programmmes will not run and you will need to update.
OS X on PPC supports classic (OS 9.2.2) programs which will run under the classic environment.
OS X on Intel does not but you can run some classic programs using Sheepshaver.