Clay soil can pose physical problems for both gardener and garden - it is heavy and hard to work (best to work it as little as possible), and often does not provide the oxygen that plant require to grow properly. Amendment helps, as does a good permanent mulch of organic material. The slightest grade can also provide a significant drainage improvement (e.g. 'berms' created on flat areas).
    Clay soil may be poor or rich in nutrients, but the soil's structure can also effectively 'lock' nutrients (such as iron) making them unavailable to plants. Organic amendment, either mixed into the soil ahead of time or applied as a mulch, is the best way to mitigate the negative effects of clay (addition of sand or gravel can sometimes make things worse!). Gypsum can also help some clays by binding the flat clay particles together to make larger, loam-like particles - this takes repeated applications over a length of time (years).

SHRUBS
Aucuba japonica
Berberis sp.
    Barberry
Buddleia sp.
    Butterfly Bush
Calycanthus sp.
    Spicebush
Carpenteria californica
Cestrum sp.
    Jessamine
Chaenomeles sp.
    Flowering Quince
Choisya ternata
    Mexican Orange
Diplacus aurantiacus
    Monkeyflower
Elaeagnus sp.
xFatshedera lizei
    a bi-generic hybrid of Fatisia & Hedera
Fatsia japonica
    Japanese Aralia
Heteromeles arbutifolia
    Toyon
Holodiscus discolor
    Creambush, Oceanspray
Mahonia aquifolium
    Oregon Grape Holly
Myrica californica
    Pacific Wax Myrtle
Nerium oleander
    Oleander
Osmanthus sp.
    Sweet Olive
Philodendron bipinnatifidum
    P. selloum
Physocarpus sp.
    Ninebark
Plumbago auriculata
    Cape Plumbago
Punica granatum (small or dwarf types)
    Pomegranate
Pyracantha sp.
    Firethorn
Rhus sp.
Ribes sp.
    Flowering Currant
Rosa sp.
    Rose
Rosmarinus officinalis
    Rosemary
Sambucus sp.
    Elderberry
Scrophularia californica
Spirea sp.
Symphoricarpos sp.
    Snowberry
Tagetes lemmoni
    Mexican Shrub Marigold
Viburnum opulus
    Snowball Bush, Cranberry Viburnum
Weigela florida

VINES
Aristolochia californica
    Pipevine, Dutchman's Pipe
Hedera sp.
    Ivy
Lathyrus sp.
    Sweetpea
Lonicera sp.
    Honeysuckle
Parthenocissus sp.
    Virginia Creeper, Boston Ivy
Vitis sp.
    Grape

MID-SIZED PLANTS
Acanthus sp.
    Bear's Breech
Agave sp.
    Century Plant
Alcea sp.
    Hollyhock
Anemone japonica
    Japanese Anemone
Artemisia sp.
Asclepias sp.
    Milkweed
Aster sp. (many)
Centaurea sp. (some)
Coreopsis sp.
    Tickseed
Dasylirion wheeleri
    Sotol
Digitalis sp.
    Foxglove
Echinops ritro
    Globe Thistle
Eupatorium sp.
Helianthus sp.
    Sunflower
Hemerocallis sp.
    Daylily
Kniphofia sp.
    Red Hot Poker
Leucanthemum sp.
    Chrysanthemum
Miscanthus sp.
    Maiden Hair Grass
Pelargonium sp.
    Pot Geranium
Pennisetum sp.
    Fountain Grass
Penstemon sp. (many)
Protoasparagus sp.
    Florist's Asparagus
Salvia sp. (some)
Senecio sp.
Solidago sp.
    Goldenrod
Yucca sp.
Zantedeschia aethiopica
    Calla Lily

LOW PLANTS
Achillea ap.
    Yarrow
Acorus gramiineus
    Grassy-leaved Sweet Flag
Anchusa sp.
Bergenia sp.
Callirhoe sp.
Campanula sp.
    Bellflower
Ceratostigma plumbaginoides
    Dwarf Plumbago
Delosperma sp.
    Iceplant
Equisetum sp.
    Horsetail Rush
Eschscholzia californica
    California Poppy
Filipendula sp.
    Meadowsweet
Galanthus sp.
    Snowdrop
Galium odoratum
    Sweet Woodruff
Helleborus (many)
    Christmas Rose
Heuchera sp.
    Coral Root
Iris (bearded, spuria, and some others)
Juncus sp.
    Rush
Leujocum sp.
    Snowflake
Ligularia sp.
Mentha sp.
Myosotis sp.
    Forget-Me-Not
Narcissus sp.
    Daffodil, Jonquil, Narcissus
Phyla nodiflora
    Lippia
Physalis alkekengi
    Chinese Lantern Plant
Ruta sp.
    Rue
Sanguisorba sp.
    Burnet
Satureja douglasii
    Yerba Buena
Sisyrinchium californicum
    Golden-Eyed Grass
Symphytum sp.
    Comfrey
Tolmiea menziesii
    Piggy-Back Plant
Verbascum sp.
    Mullien
Zephyranthes sp.
    Rain Lily