By heavy shade, do you mean no direct sun at all? Also not sure if you're looking for annuals for a seasonal display, or something that might last a few years. In Canada, such high latitude, heavy shade would be even more challenging I think. Do you bring plants in for winter at all?

There's always Coleus and Perilla for a start.

Schnookable: Like Purple said... If you tell us a little more, such as where in Canada you live, we would have a little more to go on. BC alone goes from zone 7a to 0b, which is quite a jump, hardiness-wise. -Also if it's a place that NEVER gets sun, or if you get a bit in the evening or mornings, would be a help, if we are to conjure up any suggestions ;-)
Many hostas are cold-hardy to zone 3, and get purple, pink or white flowers. -IF in zone 3, you would have to take good care when overwintering (up against a wall, covered with loads of snow). -Some varieties have bluish leaves as well.
Campanula poscharskyana (Serbian bellflower, trailing bellflower) has puple, almost blue, flowers. It will grow well in a place that gets at least SOME light (morning or evening). If you live near the coast, I think it might overwinter outside, but will otherwise do fine inside in the window. -Prefers to grow in gravel, or at least a VERY well-draining soil.

Hi Vgtar & Purpleinopp!

Sorry for the delayed response, as I have been working the past few days. I live in Toronto, Canada and my balcony receives morning sun. I face south. I am looking for a nice plant or flower to put in a spot that will only receive about three hours of sun a day. I was thinking about lungwort. I love foliage with a blue leaf as well.

Hi Vgtar & Purpleinopp!

Sorry for the delayed response, as I have been working the past few days. I live in Toronto, Canada and my balcony receives morning sun. I face south. I am looking for a nice plant or flower to put in a spot that will only receive about three hours of sun a day. I was thinking about lungwort. I love foliage with a blue leaf as well.

In Toronto, your USDA zone is 5, which would be fine for a potted lungwort with some some protection, and three hours of sun should be enough for it. Give it a lot of mulch, not only will it protect the plant from the cold, but it will also help the soil from drying out too quickly. -These plants are NOT drought tolerant!

VG

Thanks for your help Vgtar :)

Sounds like a perfect spot for various Begonias. Polka dot plant (Hypoestes.) Lobelia. If you'd like purple leaves instead of flowers, look at Persian shield (Strobilanthes dyerianus,) and Tradescantia pallida or zebrina would love it there, T. fluminensis has green leaves but tons of tiny white flowers.

In addition to the above, you can also grow foxglove, ajuga, japanese anemones, and streptocarpellas.