The fussy include peonies because they need to staked or they fall over in the rain when they're blooming. I love the way they smell and the way they look though. And they are superb cut flowers.
Delphinium fall into that class too since they need staking, are heavy feeders, want lots of water and the slugs love them too. But I love them way too much not to grow them.
I love Siberian Iris but they aren't low maintenance either.
They need to be divided every 3 or 4 years. And that's no minor process either. It takes a couple of big garden forks and a lot of muscle to break up a big clump. And of course THEN you need to find a home for the extras because it's just so hard to toss them on the compost pile.
Oriental Poppies need staking and dividing over time. I grow this lovely peach colored one that is worth the effort.
Japanese Iris are a challenge for me to grow because they like rich damp soil. I grow them in pots that have limited drainage and that seems to at least support them. I grew these from seed 15 years ago and have managed to keep them alive by dividing them every 5 years or so.
Pretty much everything else I grow is low maintenance which is pretty amazing.