Deer can damage ​if not destroy almost any newly planted plant! The text in the photo above gives some reasons why. Adult males can also damage tree trunks when they rub their antlers on them.

Before I list the plants that are highly deer resistant, I will state that virtually no plant is 100% deer resistant.
So, if deer inhabit your area, I recommend:
-CAGING all new plants, especially from flats and 1- and 2- gallon plants. Certain highly resistant plants that are planted more deeply and are in 5 gallon or larger containers may survive without caging (if deer don't trample them or gore them with their antlers!)
-Leave cages on your most deer resistant plants at least 6 months to a year! The idea is for the plants to develop a good lateral root base, have time to start producing phytotoxins, and to be less tempting due to the new smells and foliage that curious deer (and rabbits and armadillos) like to investigate. Remove one cage at a time and let them go for a few days to see what happens. If the plant gets munched but has a good root system, it will grow back.
-Plastic coated green metal wire, like the kind sold at Home Depot and elsewhere, works well. Often a single metal stake is sufficient to support this. Plastic flexible caging works well, but you will need more stakes to support this type.
-Cages should be a few inches wider than the diameter of your plant and at least a foot taller, to start.
-If you want a tree or large shrub that is NOT deer resistant, you can cage it with stacked wire cage up to about 5 feet or so, until the majority of the foliage is above browse level.

Still with me? OK, here are plants that in MY EXPERIENCE, deer USUALLY leave alone! Non-natives have an asterisk.
American Beautyberry
Anacacho Orchid
Bee Balm/Horsemint/Lemon Mint/Bergamot
Blackfoot Daisy
Bluebonnets
Burford Holly*
Carolina Jessamine
Chile Pequin/Chile Petin
Copper Canyon Daisy*
Crossvine
Damianita
Datura /Jimson Weed/Angel trumpet
Dwarf Palmetto
Elbow Bush
Esperanza, (Yellow Bells)
Esperanza, Sangria
Flame Acanthus
Frostweed
Garlic Chives*
Gaura, most types
Golden Groundsel
Honeysuckle, Coral 
Indian Blanket /Gaillardia 
Inland Sea Oats
Lantana, Native Texas
Maximilian Sunflower
Mexican Feathergrass*
Mexican Hat (Ratibida)
Mexican Mint Marigold*
Milkweed: Antelope Horns, Butterflyweed, and others
MIstflowers; Blue, Fragrant, and Gregg’s 
Muhlys: Big, Gulf Coast and Bamboo 
Nolina (all species)
Palmetto, Texas Dwarf
Prairie Verbena
Prickly Pears; Old Mexico*, Santa Rita and Spineless
Pride of Barbados*
Red Buckeye
Red Yucca
Sabal Palm, dwarf
Sage, “Lipstick” Salvia hybrid
Cedar  Sage 
Indigo Spires, Salvia hybrid 
Sage, Mealy Blue 'Henry Duelberg’ 
Sages: Autumn sage (Salvia greggi) varieties including Pink, Red, and White
Tropical Sage,
Santolina, Gray*
Sedges: Webberville and Woodland
Skeletonleaf Goldeneye
Skullcaps: Heartleaf  and Pink*
Sotol (all species)
Sumac, Flameleaf and Evergreen
Texas Betony
Texas Persimmon
"Texas Sages": Cenizo (Leucophyllum), Compact, Convent, and Green
Tree Senna
Turk's Cap
Twistleaf Yucca
Whale’s Tongue Agave  
Wooly Stemodia
Yarrows: Moonshine and others
Yaupon Holly
​Zexmenia, Orange