There's so much confusion about when to prune. All the experts and extensions have different opinions, like just about any subject on the internet. The way around this is lots of research and serious deduction. I've spent a lot of time going over this and I think I can make sense most of the time, though others may happily disagree with me about done of this.. I'll try to point out the reason for specific trees when needed, or at least TYPES of trees. You can use the same reasoning for pruning shrubs, since I don't address a lot of those.
I don't address trees grown for fruit or nuts here. I'll deal with that in another post.
PRUNING BY SEASON
Winter pruning will generally produce less stress and encourage vigorous spring growth. Easier to see most branching during winter. Harder to see dead wood. Less chance of bleeding, which may attract pests or be unsightly.
Spring pruning is ok in limited amounts, but not major pruning. Pruning will encourage bleeding in some trees, and should be avoided in oaks, elms, and birches, along with some others. The trees just want to grow during this season, and too much pruning will stress them out. It's the ideal time to do pinching and encourage proper direction, if you have the time. Some vigorous growers will greatly benefit from pinching, thus saving time pruning in other seasons. Planting is also good during early spring, and the best time for root pruning during planting.
Summer pruning will slow down growth, if you want to keep your trees from growing bigger. Easier to adjust branch leafing and balance in some cases, especially with Japanese Maples. Also easier to spot dead branches. Summer pruning is more likely to attract pests in certain species, namely oaks, elms, and birches.
Fall pruning is best avoided. Starting in about Sept/Oct., anything other than very light pruning may encourage new growth that can be harmed by the coming cold. It is, however, a good time to remove spent flowers or seeds on certain trees, especially where they make a mess, like on Crape myrtles or Chinese Pistaches. It's also a good time to plant trees, just before the rains.
DEAD, DAMAGED OR DISEASED BRANCHES
Any time you see and can get to them. The sooner, the better.
These are vertical shoots that some trees put out in response to pruning, and the more severe the pruning, the more shoots. They look silly. It's best to nix these early on. In some cases I'll leave them toward the lower end of a branch to increase girth at that location for proper tapering, but remove them before they're big enough to leave a scar. I notice these especially in plums and Chinese pistaches.
NON-FLOWERING DECIDUOUS TREES
Prune deciduous trees that are not focused on flowering in January or February, or for some species into March, or just before spring bud swelling or leafing out. You can probably include late December, if all the leaves have dropped. Trees that bleed a lot, like maples, birches and elms will bleed less or not at all in early winter. You shouldn't have to worry about the cold affecting them.
FLOWERING DECIDUOUS TREES
Deciduous trees that flower can also be pruned in winter as long as you realize that pruning BEFORE flowering will reduce the amount of flowers. However, this isn't always a bad thing. If you're doing very minor pruning, especially in the interior or at the top, you likely won't remove enough flowers to make a difference. It's also probably better for the health of the tree to make specific major cuts in winter for better recovery. The plan I suggest is to remove any larger branches or ones that don't really show from the outside in winter, and do the rest after flowering. Another important point is that much of the branching, but not all, is easier to determine without leaves or flowers on the tree. It can be a bit harder to determine what branches are dead, so it's best to prune dead wood throughout the year as you see it. With trees that flower on new wood, like Crape Myrtles, it's best to prune during the winter, with minor touchup/pinching if needed throughout the year into late summer.
It's best to prune conifers during dormancy, either winter or summer, more specificall December to February, June, or July. They'll handle the stress best during those months. Touchup can be done as needed throughout spring and summer. Pines have a specific need that's usually in May or June, where you cut or pinch the current candles back about 1/2 during the growth period to keep growth more dense and compact.
These are best pruned during winter or summer dormancy, so as to reduce stress. By dormancy, I mean that it's growing very little or not at all during this time. Growth is primarily in spring, with a bit in the fall. But some species or even specific members of a specie will have an odd growth spurt, and it's probably not the best time to do major pruning during that spurt.
INDIVIDUAL COMMON SPECIES
I'll keep adding to this list over time, so check back if you don't see what you want, or ask a question in the comments section, or e-mail me.
Arbutus/strawberry tree: Jan-Mar, June-Aug., minor pinching Jan-Oct. If needed.
Birch: Late Dec.-early Feb., to avoid bleeding. Spring & summer pruning can attract harmful pests. DEAD wood anytime. Very minor pruning or in summer only if necessary. Some branches may grow too quickly proportionally or in the wrong direction, so you can keep those in check as long as you make smaller cuts.
Conifers: Late Dec.-Feb., June-July. See "Pine" for specifics about those.
Crape Myrtle: Very vigorous. Prune Jan-March, then minor pruning & pinching through Aug or Sept. to encourage multiple branching and avoid overly-long shoots. You may lose a few pending flowers in the process, but there are usually so many that it's better to sacrifice a few for one or several years to develop good long-term form . DO NOT TOP, POLLARD, LIONTAIL OR REMOVE ALL LOWER SECONDARY BRANCHES. If this has already been done, there are specific remedies that will be addressed in another post. You may also prefer to remove the spent flowers as they dwindle. This may or may not encourage a second round of flowers.
Elm: Late Dec.-early Feb. to avoid Dutch Elm or other disease from bleeding. Dead wood anytime.
Flowering cherry, plum, apricot, almond, etc.: Usually May-July, to keep flowers, but I think major pruning that won't undermine flowering is best in Jan.-Feb. Keep in mind that plums get substantial vertical water sprouting after major pruning and to a degree after minor pruning, and it's usually best to remove these as early as you can by rubbing off, pinching, etc.
Maple: Late Dec.-early Feb., May-early Aug . Very vigorous growth in Spring. Minor pruning/pinching Jan.-Sept.
Oak: Late Dec.-Feb. Pruning other than dead wood during the rest of the year attracts pests.
Pine: Dec.-Feb, June-Aug. major pruning, trimming candles in May/June at their peak.
Sycamore: Late Dec.-early Mar., June-Aug.