Lot of the winners (and non-winners) have gone on to successful careers. Just depends on how you define successful. To me if an artist can make a living at what they love and have artistic choice in what they do then that is success. To others, they have bombed if they aren't on the celebrity gossip rounds and don't have mega-popstat status. That just seems a bit of a narrow view to me.
post-idol commericial success rankings is probably:
Underwood - I don't get country but there you have it...she sells
Clarkson - hit the genuine 'popstar' label and sold a ton, probably some of the success was that she was the first idol
Daughtry - has sold a lot of albums and frequently on the radio
Lambert - couple of successful albums and the second one was actually good, some acting, toured with queen to sold out arenas and raving critical/popular reviews
Hudson - having an oscar doesn't suck
P^2 - hit the timing right with the song written for him. sold tons
Sparks - still see her popping up here and there both in acting and music
McPhee - not music but doing well her tv gigs it would appear
Beyond those there are a ton who are doing well in the industry even if you haven't heard much of them - Cook, Allen, Archuleta, McCreery, Barrino, Gokey, etc. Some on Broadway as well.