Common potato salad add ins in my house: bell pepper, red onion or shallot, celery, olives, dill pickles, fresh parsley. That's cold with a tangy mayo/yogurt dressing.

Lately we've been having hot potato salad, closer to a German potato salad, where you pour an oil & vinegar dressing over hot potato cubes, and smother it in chopped parsley. The hot potatoes suck up the dressing and get kind of creamy.