People are asking more and more for plants that do well in the shade, and luckily in Utah we have many options beyond the begonia and impatiens staples.
Jim Horrocks, a local fern expert, says that many ferns can be successfully grown in Utah when grown in "humus-rich soil that is kept well mulched to conserve moisture and keep the soil cool."
Although spring flowering bulbs prefer the sun, if planted under deciduous trees (trees that lose their leaves during the winter), the bulbs will bloom and be able to replenish their storage before heavy shade is attained for the season.
A final tip before you begin, not all shade is the same. If you can only provide shade during part of the day, protection from the west or south is typically the most critical. The sun's rays from the south and/or west are more intense and can be more damaging to shade loving plants. Many plants that love partial shade can handle full sun on eastern or northern exposures. Also note that Utah's sun is more intense than other climates, some plants that may take full sun in the east, may benefit from partial shade in Utah.
The following links are lists of shade-tolerant plants: