Whether you collect blue flowers and enjoy the unusual, or need just the right blue flower for your patio, deck or flower garden, you should find something to love among the following very special blue flowered plants.
Agapanthus or Lily of the Nile is not winter hardy in many parts of North America, but it can certainly be grown as a container plant to provide an exotic display of magnificent blue blooms. And in areas where it is reliably hardy, Agapanthus is a low maintenance yet high performance plant worthy of any blue flower garden.
Evolvulus is another tender perennial (winter hardy to USDA zone 9) that does very well as a container plant and is often sold as a specialty annual; you might see Blue Daze or Hawaiian Blue offered for sale. This is one of my favorite blue flowered plants.
Plumbago auriculata thrives in heat and is only winter hardy in zone 8B and warmer, so again it would be a candidate for container growing (with regular pruning) in colder areas. Flower color ranges from pale to medium blue. When grown in the landscape, this plant can be trained as a shrub or as a vine.
Lithodora diffusa "Grace Ward" is an amazing blue flowered perennial, so striking it is absolutely irresistible when you see it. Keep in mind it is not easy to grow. It is winter hardy only to zone 6 but if you have hot, humid weather in summer it dies out. I fell for it three times before I gave up. It might do well for gardeners in the Pacific Northwest. Or perhaps you will like it enough to grow it as an annual.
Another difficult to grow plant with amazing blue flowers is the Himalayan blue poppy, a Meconopsis. These need very specific growing conditions in order to thrive. So specific, they are rarely seen in gardens at all. I understand they are grown at the Jardins de Metis in Quebec, where they apparently like the cool summers and manage to survive the winter beneath the thick blanket of snow. I have seen the isolated one or two in public gardens on the east coast over the years, where I suspect they were the resident horticulturist's pet curiosity, but never an ongoing planting. So while I would not discourage you from trying, don't be too dismayed if you fail.