The most important thing to remember when dealing with plants is not to disturb active roots. That means that you shouldn't dig a plant any old time. Instead digging should be limited to the early spring or late fall when the plant is dormant. The time to dig a plant, especially woody plants like trees and shrubs is critical.
So what about planting? Is the timing just as critical for planting as digging? Simply stated: No. Since pretty well all plants are purcahsed in a self contained pot, you really aren't disturbing the roots. That basically means you can plant trees, shrubs, perennials, annuals, or whatever else pretty near any time of year, providing you can work the soil.
So is one time better than the other? Most commonly spring and fall are touted as the best time. Personally, I always say as early as possible. My reasoning is simple: the earlier you plant something in the year, the more time it has to make roots and prepare for the winter.
Planting early spring has a number of advantages. You can the top selection of plants since there aren't as many odd-ball plants around so they can sell out quickly. The cooler weather means less watering. Since the plants are naturally just waking up, they feel less stress and naturally want to form new roots. As the season progresses, they look pretty so we tend to maintain them a little more. All in all, I like spring the best.
There's nothing wrong with summer planting, either. Plants are actively growing and still making roots. Transportation of larger trees needs a little more care since you don't want the leaves to burn off in transport. Watering is more critical since it's warmer out and a plant's root-ball may dry out faster than the surrounding soil. But summer is an excellent time to add to the perennial garden since regular visits to the garden centre help us see what's in flower at different times of the year.
Fall planting can work great, but generally the plant have less time to make roots. That, and fall planted stock tends to be a little more ignored since it doesn't look as pretty. Your selection is also much more limited in the fall as some varieties of plants get sold out. If you're hunting for a deal, it may work, but you may also lose out on the perfect plant. Make sure anything planted in the fall gets ample water before freeze-up happens. You can plant right up until the ground freezes, providing your plant's roots remain wet.
And one last comment about planting: Do not disturb the roots! I have no idea why there are so many articles out there about breaking apart the root ball and spreading the roots. If you want to stunt a plant, that will do it. Try that with a tree in the summer and you're sure to kill it. Just don't do it. Leave the root ball the way it is and plant it whole. Your plant will thank you.