I like gaillardia for its long season bloom, but should be dead headed. New England Aster is tall and will spread by seed. I dead head as soon as the flowers fade. Japanese anemone bloom late and will spread, Alyssum is an annual, but reseeds Helebores in shade, bloom early and only grow larger. Knock-out roses bloom all season and require little attention. Different colors, too. Heucheras flower, but are grown primarily for their foliage. Large variety. Ladies Mantle also has interesting foliage after the flowers fade. Should be deadheaded to prevent seeding. Hardy Hibiscus needs little care and lasts for years.
Hope this helps. These are a few that have worked for me with minimum care in the Akron OH area.
Herman

In my SE WI garden Asiatic lilies come back if in a sunny location. Tiger lilies do, too, and tolerate some shade. Hens and chicks would fall under the category of your sedum: they survive even in heat or cold, wet or dry. Black eyed Susans bloom when much of the summer color has gone, and they bridge the span up to the blooming time of mums.

Hibiscus syriacus, aka Rose of Sharon and Hibiscus moscheutos -- both types of winter hardy hibiscus -- form nice flowering shrubs in a sunny location, and IME, are quite low maintenance.

For shade you can't beat Solomon's Seal. The arborescens and paniculata type hydrangeas are easy care and great bloomers. Carpet roses need deadheading but are otherwise easy care.

Shade : Solomon seal, and it comes in a varigated form as well as the non vargiated. For something tall in shade, I like monkshood (poisonous) and Lingularia (not poisonous), but there is a trick to planing lingularia because it likes moist soil. Dig down an extra foot or more, lay down a plastic bag, then backfill until you reach the planting level. This makes the dirt under the roots stay nice and wet. Anenomes are beautiful, who cares if they tend to spread, they are forgiven because they are so lovely.
In sun, I wouldn't use gallardia for a maintence free garden because they must be deadheaded, or they stop blooming and reseed everywhere. Low, ground hugging sedums are better, coral charm, lidakense, pork and beans. there are too many to list. All low water, full sun, and maintence free.
Northern Wisc. zone 5

It's a good list. I would add coreopsis to the list of tough flowering plants for full sun and low water.

For shade, try wild ginger. It needs a little water while getting established. Once it's set, it's a low maintenance ground cover.

Veronica and salvia. herbs are quite easy in dry sunny neglected spots[lavender!] russian sage. epimedium fills in-likes some shade. Coneflower-newer colors-sun. yarrow!

What about bulbs like daffodils, which are rabbit resistant?

I'd add: Hardy Hibiscus and Hydrangea. Both appear pretty bullet proof in my hands and the flowers are so gigantic and last so long, you just can't help but feel you've done something right! :-)

I am a lazy gardener without a lot of money. Gardening in pure clay in the St Catharines area. I know bulletproof! Ok, the best by far is scarlet Flower Carpet roses. No pruning or deadheading needed and after 4 years they are 4 ft tall and wide and bloom June to November, continuously and abundently. Water while establishing, but after that just let them go. A lot of the above I agree with but would add hardy geraniums, tradecantia, sweet william sooty, bachelors buttons,delphiniums, marigold (self seed), chives, perskovia, silver beacon lamium, red nancy lamium, and add some great shrubs like spirea, diablo ninebark, purple leaf sandcherry. The lamium and transcantia are great for shade. My hydrangeas are great but are the only thing that requires extra watering. Oh and don't forget columbine.