From the south, moving north.. to Canada.

(Ozark) (not considered part of the Appalachians, but actually from a geological point of view, should be)
North Georgia mountains (edited, as per AS!thanks)
Cumberland
Smokey
Blue Ridge
Shenandoah
Catoctin
Allegheny
Kittatinny
Poconos
Catskills
Adirondack
Berkshires
Green
White Mountains
Katahdin
Longfellow
Notre Dame(Quebec/Newbrunswick)
Long Range (Newfoundland)

Foot Hills and Highland associated with the Appalachian's (incomplete, to say the least)
Piemont Plateau (extends into Alabama)
Watchang
Ramapo
Cape Breton Highland

In Scotland/ Wales?
Cambrian?
Grumpian?

i am sure that there are more...