Janeen Adil,in Accessible Gardening, makes some good suggestions for plants
in vertical gardens...
In the tomato category, she recommends Better Bush and Husky varieties.
PEAS, BEANS, AND CUCUMBERS
These peas grow 4'-6' high and are good for people who can't bend...
Tall Telephone (or Alderman)and Multistar for "regular" green peas.
Sugar Snap and Mammoth Melting Sugar for snap peas.
Norli and Carouby De Maussane for snow peas.
Since pole beans prefer to be grown vertically, the only real consideration is total height at maturity. There are varieties that will get 10' tall, so read the packaging carefully!!
Many varieties of cucumbers do well climbing. Consider planting the seeds
along the outside of a cage.
Melons and Squash
The biggest issue with growing
vertically is the size of the fruit.
Minnesota Midget Cantaloupe
Yellow Doll Hybrid Watermelon
Butterbush Winter Squash
Long Green Striped, Zuccetta Rampicante and Tromboncino are special varieties of summer squash that can be grown vertically.
Jack Be Little and Baby Boo are miniature pumpkins that do well vertically.
FLOWERING AND ORNAMENTAL VINES
climbing sweet peas (Lathyrus odoratus)
black-eyed-Susan vine (Thunbergia alata)
climbing nasturtium (Tropaeolum majus)
morning glory (Ipomoea purpurea)
scarlet runner bean
moonflower (Ipomoea alba)
wisteria (Wisteria floribunda)
trumpet vine (Campsis radicans)
silver lace vine (Polygonum Aubertii)
climbing hydrangea (Hydrangea anamola)
jasmine (Jasminum officinale)
perennial sweet pea (Lathyrus latifolius)
passion vine (Passiflorax alatocaerulea)
Dutchmen's pipe (Aristolochia macrophylia or A. durior)
bittersweet (Celastrus scandens)
Virginia creeper (Parthenocissus quinquefolia)
Boston Ivy (Parthenocissus tricuspidata)
English Ivy (Hedera helix) rose (Rosa)
glory vine (Vitis Coignetiae)
common grape (Vitis vinifera)
fox grape (Vitis Labrusca)