Any time after about mid September.......and right on through winter in most cases, weather dependent.

Depending upon how well-developed is well developed...you may find it easier to either take cuttings or buy new plants and just get rid of your current ones.

You might be amazed at the roots on some of these, and also phazed by low survival rates if most of the root mass is lost.

Not saying you cant...just if they've been in the ground and are mature specimens, they may not move well at all.

Thank you all for the advice.

Here's a few tips I've picked up over the years.

A sharp shovel makes it easier so you cut the roots rather than tearing them apart while pulling the shrubs up. Dig the holes first where they will be going so the time spent out of the soil is less. Use a tarp or wheelbarrow rather than carrying them by hand. Do not strain the trunk or trunks.

Wonderful advice - thank you Mike.

Leave deciduous shrubs until after the leaves drop. Many of these will still be in leaf during Sep. If any are large it is preferable to bare-root them and move then with minimal soil - but a lot of roots - instead of chopping the roots down to a small size in order to get an intact soil ball, that is of manageable weight.

What are they? If they are Rhododendrons or Azaleas they move easily, small shallow root systems, at least in my experience.