The question that I'm asked most often is, "What will grow in the shade?" There are lots of full-sun plants, but shade-tolerant plants are much rarer. Your local nursery will most likely recommend hostas and ferns. But what about flowers?
In general, foliage plants are more shade-tolerant than flowering plants. And there are more perennials for shade than annuals. Most "shade-tolerant" plants actually prefer part shade. Very few plants can survive in full shade. A few hours of direct morning sun is ideal. Filtered sunlight coming through the leaves of trees is also good.
Other factors to consider are soil quality and water. Most shade-tolerant plants enjoy rich, moist soil. But some will survive in moderately dry, poor soil. Sometimes, you just have to experiment to see which plants will work in your garden.
Here's a list to get you started. Obviously, there are many other shade-tolerant plants (like good old hostas). This list only includes flowers that can be grown from seed and are available for sale on this website. The amount of sun required varies, but all of them should grow in light shade, and a few of them can tolerate dense shade.