Native palms are those that grow naturally in a certain area and have adapted to that area’s climate, fauna, and surrounding environment.  Florida has the largest variety of native palm trees in the continental US.  Hawaii has the largest variety of palms of all 50 states.  North Carolina has the most northerly-growing palms (in natural habitat). 
Following is a list of all palms native to the US (no species are repeated).
Palms native to Florida, Georgia, North Carolina, South Carolina, & Louisiana:
1) Cabbage Palm (Sabal palmetto)
Most common palm.
2) Dwarf Cabbage Palm (Sabal minor)
    From northern Florida and Southeast US.
3) Miami Palmetto Palm (Sabal miamiensis)
    Nearly extinct in wild.
4) Scrub Palmetto (Sabal etonia)
    Like Sabal minor, but with arching leaves.
5) Saw Palmetto (Serenoa repens)
    Fruit used to make prostrate supplements.
6) Needle Palm (Rhapidophyllum hystrix)
    Most cold hardy palm in the world (-15 deg F).          
7) Royal Palm (Roystonea regia or elata)           
    Tallest native palm (100 feet).                                
8) Thatch Palm (Thrinax radiata)
    Native to Florida Keys.
9) Key Thatch Palm (Leucothrinax morrisii)
    Also native to the Kays; used to be Thrinax morrisii).
10) Silver Thatch Palm (Coccothrinax argentata)
    Found in the Keys, bluish leaves.
11) Cherry Palm; Buccaneer Palm (Pseudophoenix sargentii)
    Native to Long Key and Elliot Key; slow growing.
12) Coconut Palm (Cocos nucifera)*
    World’s most common palm.
13) Everglades Palm; Pouritis Palm (Acoelorraphe wrightii)
    Native to the Everglades.
Palms native to Texas:
14) Texas Palmetto Palm (Sabal mexicana)
    A larger version of Sabal palmetto.
15) Texas Hybrid Palmetto Palm
    (Sabal Xtexensis; Sabal mexicana x minor)
    A naturally-occurring hybrid.
Palms native to Arizona:
16) Sonoran Palmetto (Sabal uresana)
    The blueist leaves of any Palmetto Palm.
Palms native to California:
17) Blue Hesper Palm (Brahea armata)
    Blue and green forms exist.
18) San Jose Hesper Palm (Brahea brandegeei)   
    Older stems display strange leaf base scars.
19) California Fan Palm (Washingtonia filifera)       ooProduces more seed in one infructescence than any      oopalm- up to 30,000.
20) Mexican Fan Palm (Washingtonia robusta)
    Grows to over 100 feet tall.
Palms native to Hawaii:
21) Pritchardia affinis
22) Pritchardia arecina
23) Pritchardia aylmer-robinsonii
24) Pritchardia beccariana
25) Pritchardia flynnii
26) Pritchardia forbesiana
27) Pritchardia glabrata
28) Pritchardia hardyi
29) Pritchardia hillebrandii
    Blue and green forms exist.
30) Pritchardia kaalae
    Native to Oahu.
31) Pritchardia lowreyana
32) Pritchardia maideniana
33) Pritchardia martii
    Native to Oahu.
34) Pritchardia minor
35) Pritchardia munroi
36) Pritchardia napaliensis
37) Pritchardia perlmanii
38) Pritchardia remota
39) Pritchardia schattaueri
40) Pritchardia viscosa
    One of the most endangered palms on earth.
41) Pritchardia waialealeana
    Comes from Mt. Waialealeana- the wettest place on earth.
* Although considered by the state of Florida to be native, Coconut Palms are thought to have originated in the South Pacific and Malay Peninsula.  They have been in Florida for centuries however, which “grandfathers” them in.