I don't think you can ever reach the no iron holy grail. However I never iron, jeans, t-shirts, knitwear, school shirts etc. The trick for me is firstly don't leave the clothes in the washing machine after the was for too long (more than an hour). Then shake out each item as you put it in the tumble dryer, uncrumble twisted legs on jeans. Most important step is to remove from the tumble dryer within a few minutes of it ending. Take each item out, shake, fold and then smooth down with your hands.
Job done.
Linen items, shirts are about all I iron.