Out of control lists:

Gorse and pampas grass, poison hemlock and yellow star thistle, Scotch broom and German ivy, red-apple aptenia and blue-gum eucalyptus

giant thistle cardoon, and fennel

broom, pampas grass (both the Cortaderia jubata evildoer and the less-invasive C. selloana), fountaingrass, water hyacinth

Reasons...

Another article and web sites

-- Ailanthus altissima (tree of heaven);

-- Arundo donax (giant reed);

-- Centaurea melitensis (tocalote);

-- Cirsium vulgare (bull thistle);

-- Cortaderia jubata (jubata grass, miscalled pampas grass);

-- Senecio mikanioides (cape ivy);

-- Spartium junceum (Spanish broom);

-- Tamarix chinensis, T. gallica, T. parviflora, T. ramosissima (tamarisk, salt cedar).

-- Red-apple aptenia (Aptenia cordifolia);

-- Licorice plant (Helichrysum petiolare) -- these two are not widespread, yet, but show potential;

-- Pennyroyal (near wetlands);

-- Water hyacinth, parrot's feather, and elodea or anacharis if you're next to fresh water;

-- Periwinkle (Vinca major);

-- Capeweed (Arctotheca calendula);

-- Cape or German ivy (Delaira odorata or Senecio mikanioides);

-- English ivy (good old Hedera helix);

-- Ox-eye daisy, or marguerite;

-- Foxglove (if you're near a damp area or stream);

-- Purple loosestrife -- illegal to sell in some states;

-- Fennel;

-- Woolly mullein;

-- Fountaingrass (Pennisetum setaceum);

-- Pampas grass;

-- Broom of all sorts;

-- Gorse;

-- Tamarisk;

-- Myoporum;

-- Russian olive;

-- Ailanthus;

-- Blue gum eucalyptus;