If you are talking about on the 360 and not the pc, you HAVE to get a gamepad or encoder board that has the analog stick inputs to use them..... you don't have any other option. Hack a cheap knock-off pad if money is the issue.
That being said, games that don't use the d-pad are probably games that need analog inputs, so they aren't going to be fun to play on a digital joystick anyway.