I love plants that give second life! By that I mean plants that can be cut back in the middle of the season only to be reborn again weeks later for that second burst of flowers. Some will also take a third cutting to give that last push into Fall.
Nepeta 'Cat's Pajamas' my favorite, is a perfect example of that. I'll cut back in early May, then late July and again early/mid September to let it ride out the Fall.
Now when I say cut back, this all depends on the type of plant. Nepeta, I'll cut back to the new growth emerging at the bottom, whereas something like Heuchera, I will cut off the flower stem at the bottom to promote new flowers. I suggest looking up your plant on the web before the shears meet the stem. An important aspect to cutting things back is to keep up with your watering which can accelerate new growth.
There are many but here are some lovely favorite perennials and shrubs that can be born twice!
Perennials: Coreopsis, Aster, Scabiosa, Salvia, Dianthus, Geranium, Heliopsis, Monarda, Veronica, Echinacea, Rudbeckia, Dicentra, Gaillardia, Leucanthemum
Shrubs: Spirea, Abelia, Roses, Deutzia, Weigela