It is a good idea to grow plants on top of pergolas. But it is advisable to choose the right kind of plants. Some of the flower plants attracts bees and should be avoided so that you are not forced inside by a swarm of bees. Flower plants that have thorns are also not recommended, especially if you have children who play around the pergola. Fruit plats are better and useful and highly recommended, especially grape vines. There are certain types of plants that shed their foliage in winter and grow leaves in summer, these are great because they will help provide shade under the pergola in summer, but let light in to warm up winter afternoons.