Many shrubs need to be pruned on a yearly basis to maintain health. But getting to know your plants is a slow process, often involving a few initial casualties. As a general rule of thumb, plants that flower early in spring or flower on old wood (previous season's growth) should be pruned immediately after they flower. Plants that flower on new wood (current season's growth) can be pruned in late winter or early spring. Here is an overview of what to prune and when. These are guidelines for Zone 6 and higher.
There are a number of plants that respond well when pruned back hard every year in winter to early spring. They tend to produce vigorous new growth and more flowers. Some classic examples are repeat-flowering roses (e.g. hybrid teas and modern shrub roses), butterfly bush (Buddleja davidii), and blue mist shrub (Caryopteris). The first season, leave the shrub alone. The following year, when buds swell around mid-April, cut the stems back, leaving two or three buds per stem. Every subsequent year, follow the same procedure. Clean out the deadwood as well. This pruning technique will create a multi-stemmed candelabrum of stumps sprouting a multitude of vigorous new shoots that grow into a shapely and floriferous shrub each year.
Some shrubs are planted for a specific effect: pussy willows (Salix) for the catkins and red-twig dogwoods (Cornus sericea) for the ornamental stems. Cutting the majority of the stems back hard (down to 6 inches for the pussy willow and to the ground for the dogwoods) ensures that you will have vigorous new growth with bright color and plenty of catkins. Beautyberry (Callicarpa) also benefits when its oldest stems are cut to 6 inches in late winter so that the plant can send up new growth covered with glorious purple berries.
Some shrubs flower on old wood and produce beautiful ornamental berries. In these cases, you can either prune immediately following flowering or prune lightly in early spring. Either way, you will be reducing the amount of berries. Some examples are scarlet firethorns (Pyracantha) and many viburnums (Viburnum).
It's important to get to know your shrubs. Daphne (Daphne) resents being pruned. It is short-lived in the NYC area, performing well for 3 to 5 years and then quickly fading. Witch-hazels (Hamamelis) can be cut back hard but prefer to be handled gently; these long-lived shrubs have a beautiful vase shape and are generally best left alone. English boxwood can be sheared to your heart's delight once the weather warms, but it's important to stop late in the season so the foliage can harden off before the cold.
Here is a list of the best times to prune your trees and shrubs. Before you prune, make sure you have comfortable, sharp, clean, pruning tools to work with.