I don't know about low water, but moderate watering has a lot of possibilities. Cannas love full sun and lots of water, but they do well with moderate water. Others that come to mind are: Peace Lily, philodendrons, hibiscus, Night Blooming Jessamine, elephant ears, some ferns can be low-mod water, Star Jasmine, bird of paradise.

Good Luck,

Karen

Here are few ideas:
Aspidistra elatior - Castiron plant
Ficus carica - Edible fig
Catalpa sp.
Eriobotrya - Loquat
Philodendron selloum
Paulownia
Polystichum munitum - Western sword fern
Acanthus mollis

I'm not sure exactly what zone you're in, but in southern California you should have a lot to choose from. Many palms are drought-tolerant and one of the best for your area would be the european fan palm, Chamaerops humilis. Other possibilities are plumeria, oleander, many cycads (esp. Cycas & Zamia species) and bird-of-paradise. Strelitzia nicolai has very large, tropical-looking leaves (a good banana substitute but more drought tolerant) although the flowers aren't as showy as those of S. reginae.

Ooh. Take a drive to San Diego's Balboa Park and check out their "cactus garden". You'll see most of Johnnie B's suggestions there, plus various cactuses and relatives and South African natives like proteas and leucadendrons. And clivias and agapanthus. Although people tend to think of jungles whe they think tropical, all these guys are (sub)tropical too. And very appropriate to LA.

Many of the plants other members named above need lots of water! I live in Fresno so i know what you mean by low-water, especially with less than 10 inches of rain per year. Here are some plants that i grow and use a fairly low amount of water.

Bougainvillea and Bird of Paradise. Bougainvillea blooms best with low amounts of water.
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For dry shade, try kentia palm, blechnum gibbum, clivia miniata, was begonia...
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Confederate Jasmine. You could also use Madagascar Jasmine, but that one requires a bit more water.
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Pygmy date palms, White Bird of Paradise, Pachypodium Lamereii, Pelargoniums, Agave Attenuata, Agave Desmetiana, Aloe Ciliaris, Aloe Striata, Aloe Ferox, Tree Aloe...There are TONS of Aloes and Agaves that give you the tropical look and require little water. I have all of these growing in the corner, but they are still young seedlings so it will be a couple of years before they become noticeable plants. When they do, they will be definite show-stoppers.
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Callistemon Citrinus
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Yucca Elephantipes, Ponytail palms
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Another drought-tolerant corner. Again, most of the plants here are still young, some are seedlings, but heres a list of plants growing here: Duranta Repens, Pomegranate tree, ponytail palms, several Aloes and Agaves, Tecomaria Capensis, Tecoma Stans, Mini roses, Brugmansias, Jubaea Chilensis (Chilean Wine Palm), Washingtonia Robusta, Plumbago, Lemon Guava, Clerodendron Ugandense, Coral Vine...
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these are just a few examples of plants you could use.

"Many of the plants other members named above need lots of water!"

I re-read the list, and I'd have to say: "A FEW of the plants other members named above need lots of water!" MOST don't; at least they don't in my garden (and I'm 20 minutes away from you in Madera.) And BTW, MANY of the plants you mention are also cited by other members.