The only ones I can think of right now are certain roses. But I'm no rose expert, so can't give you specific varieties.

One is Bonfire Euphorbia. It changes with the seasons, starting in the spring. I found it at Dutch Gardens under their perennials. Absolutely beautiful looking! I am planting it this fall. Will see how it goes though!
Note: the plant is toxic if eaten.
However, I don't have any pets outside, or young children to worry about.

I can think of a few shrubby things that do this, such as Brunfelsia pauciflora, Rosa chinensis var mutabilis, Brugmansia 'Charles Grimaldi', and flowering grasses such as Pennisetum moudry and P. setaceum var rubrum. Sedum spectabile and several other Sedums also change color or are lasting as dried out flowers at the end of the bloom season.

Dahlias! Many start out one color and then change as they open. Also some of the daylilies. For some reason the peachy colored ones change with light each day. I'm thinking of Sarah Joy for example which can range from peach to med purple depending on the days light and water.

Some other things that 'change' with the season would be Caryopteris, esp the yellow foliaged ones like Worcester Gold that is a light yellow foliage all summer, then in late August puts out tons of med true blue flowers. Also the shrub Hypericum Albury Purple which has dark purple tinged foliage, yellow flowers which go to red berries, then this time of yr the red berries turn black.

Gentian - another true blue with burgundy foliage is another beautiful plant late in summer.

My pulmonaria change from blue to pink as the blooms age. Certain of my hydrangeas do as well.

I realize this is the perennials forum but some Profusion Zinnias change color (the pinks, oranges, and reds I believe). I have a red-orange variety that starts out an intense solid color then unevenly fades over time to lighter, rich, orange and yellow-orange with some darker red-orange mixed in. I have heard some criticism over the fading, but I love it. When they fade they look as though they are a water color painting with all the different variations color blending into each other. I don't know how long they take to change color. At the start of the summer it was quite fast under a week but now they are more established it takes a bit longer but I can't give you precise time frame. I will try to upload a picture later to give you a sense of the beautiful coloration.