I've had a trackball for my Amiga and used it to play some (usually less action-oriented) games. I know they still exist, but they look differently, they're not completely analogue anymore and obviously that's an ultra niche market.
None of them. I can't think of any control method I miss compared to just using a modern gamepad.
The only game on DS I played that I think would have been significantly worse without the stylus was Nintendogs. There are other games that wouldn't work without it like Pokémon Ranger but I don't really care about that.
Another old gaming controller from back in the day which I loved at the time was the touchpad which came with Star Raiders for the Atari 2600:
Star Raiders was a fairly simple game in hindsight, but man at the time it was so advanced, using multiple buttons to control game features. Kind of the first space flight simulation game ever released, in a time before personal computers really existed, in a time before the game Elite.