Non-flowering plants are usually grown as foliage houseplants. They have interesting leaves and design and aren't used for flowering ability. Some of these are nice for office plants as well. Plants that do not bear flowers can still be great plants for any garden, as foliage backdrops or as an under-tree complement.
The prayer plant, Calathea ornata, is a perennial that has 3-foot-long leaves with purplish green hues. Stripes start pink then fade to white as the plant ages. It has no flowers and is used as a greenhouse or home foliage plant. It does well in high humidity and bright indirect sunlight. Soil should stay moist. Propagate via spring division. Keep this one away from drafts.
The common maidenhair (Adiantum capillis-veneris) is a fern with foot-high leaves and small leaflets. It does not flower and is grown for its foliage for home and greenhouse. It likes a high humidity and bright indirect sunlight. Soils should be drenched then allowed to get moderately dry. Propagate via spores in spring or by division in spring.
The plover eggs (Adromischus cooperi) are a succulent. Leaves are one inch long and clustered. There are no flowers and it has no fragrance. It prefers low humidity and full sun conditions with watering any time the soil is barely moist. Propagate via spring or summer leaf cuttings. Don't over-water and make sure there is plenty of ventilation.
The Japanese boxwood (Buxus microphylla japonica) is a shrub. Evergreen and small, it has little leaves and no flowers. It is not fragrant but makes a good hedge shrub. It likes medium humidity and full sun. Soil should be moist. Propagate via spring stem cuttings. Prune anytime.
Hart's Tongue Fern
The Hart's tongue fern (Asplenium scolopendrium) is a fer characterized by its wavy-edged leaves. There are no flowers and no fragrance. It likes high humidity and full sun conditions. Keep evening moist soil around the plant. Propagate via spring spores.
The silver evergreen, Aglaonema commutatum, is a perennial with marked leaves 6 to 18 inches long. They are upright and in different varieties. There are no flowers and no fragrance to the houseplant. It likes low humidity and bright indirect light. Keep soil moist. Propagate via spring division, seeds or stem cuttings.