Well Ian, we don't see too many joystick games these days anymore. 3rd party peripheral manufacturers still make joysticks for fighting games and the like, but its no longer a standard feature for any default controller, and hasn't been since the days of the Atari. The D-Pad effectively killed it off, because with the D-pad you have the same basic functionality, except you can do it with just one thumb instead of tying up your entire hand. This meant controllers could add in other buttons for more ways of controlling your character on-screen.
I think the thumbstick pretty much replaces both, though. Last night I was playing MK II and SF II on a friend's PS3 and I COULD control it the old school way with the D-pad (albeit Sony's crappy D-pad), but I quickly found the analog stick works just as well, and in fact even better.
So if the analog stick can handle traditional D-pad games just as well or even better than with the D-pad then why bother keeping the D-pad?