Pruning is one of the most useful things you can do for a tree or shrub, and one of the easiest to get wrong. The right timing depends on when the plant flowers and how it grows.
Spring bloomers like rhododendrons, azaleas, lilacs, and forsythia set next year's flower buds soon after they finish blooming. Prune them right after the flowers fade, in late spring or early summer. Prune them in fall or winter and you'll cut off next spring's show.
Most deciduous trees, including Japanese maples, fruit trees, and ornamental cherries, are best pruned in late winter while they're dormant. Without leaves you can see the branch structure clearly, cuts heal quickly once spring growth starts, and there's less risk of spreading disease.
Hedges such as laurel, privet, and boxwood can be trimmed in late spring after the first flush of growth and again in late summer. Arborvitae and other conifers should only be trimmed on green growth. Cutting back into bare brown wood usually won't grow back.
Any time of year, it's fine to remove branches that are dead, broken, or rubbing against the house or roof. If a limb is large or close to power lines, call a professional rather than reaching for a ladder.