In our area, most woody plants and perennials can be successfully transplanted anytime between mid-fall to early-spring. The trick is to avoid the stressful, hot summer months with plants that haven't had time to regrow their severely compromised root system. Pot-grown plants, that aren't pot-bound so as to require significant root manipulation at planting, can be safely planted pretty much anytime. Some species, especially some with fleshy roots (like pawpaws and some/most magnolias), do much better if planted in spring, rather than fall or winter. Also, marginally-hardy plants may have a better chance of survival if planted in spring. Plants like daylilies and rhizomatous iris usually do well if planted in spring or summer.

It's hard to talk about a generalized ideal planting time for a wide variety of plants because different plants have different requirements. Specifying a certain type of plant might lead to more specific and accurate recommendations.