Gould’s Emerald, also known as the Caribbean Emerald, was described in 1860 based on a single specimen of unknown origin; however, it is somehow believed to have originated from the northern Bahamas or from Jamaica.
Thes species was thought to be a hybrid until 1999, when its status as a distinct species could be proven. 
Since no additional individual could ever be traced, Gould’s Emerald is clearly extinct now.
 André-Alexander Weller: On types of trochilids in The Natural History Museum, Tring II. Re-evaluation of Erythronota (?) elegans Gould 1860: a presumed extinct species in the genus Chlorostilbon. Bulletin of the British Ornithologists’ Club 119(3): 197–202. 1999
Bell’s Woodnymph is a hypothetical, yet very likely real species of hummingbird that apparently was endemic to the island of Dominica in the Lesser Antilles, where it seems to have been restricted to the rainforests of the highest mountains.
The species might have been on the brink of extinction when it was discovered and described by Alpheus Hyatt Verrill, an American zoologist, in 1905 (?).:
“Upperparts rich iridescent metallic green, becoming deep peacock blue or verditer-green on ferhead and crown; coppery on shoulders and deep bluish or emerald green on rump: scapulars, upperwing-coverts and uppertail-coverts, deep peacock or bluish green. Wings metallic purple or steel blue, the outer web of outer primary narrowly edged with white or pale ash grey. Basal portion of tail dull copper green, the outer half deep steel blue with violet reflections. The three outer feathers on each side broadly tipped with white and the outermost feather white at base also. Lower parts uniform snow white or less washed with greyish on flanks and sides. Flanks and sides beneath wings spotted with isolated bright green feathers. Ear-coverts and loral region deep velvety black in marked contrast to green of occiput. Bill dusky black with lower mandible slightly lighter near base.” 
No one else did ever see this species and it apparently was extinct shortly after the abovementioned account.
The description appears to be very extensive and correct, and I personally have no reason to doubt the former existence of such a species.
 A. Hyatt Verrill: Additions to the avifauna of Dominica. Notes on species hitherto unrecorded with descriptions of three new species and a list of all birds now known to occur on the island. 1905?  Julian P. Hume: Extinct Birds: 2nd edition 2017
Alfaro’s Hummingbird was described in 1896, it is known from a single specimen that had been collected at the Volcán de Miravalles in northwestern Costa Rica; it was mostly treated as a subspecies of the Indigo-capped Hummingbird (Amazilia cyanifrons (Bourcier)) which, however, is endemic to Colombia.
The sole specimen was analysed at least two times, in both cases with the same result: it is a distinct species. 
Alfaro’s Hummingbird is now accepted as a full species and is considered extinct.
 André-Alexander Weller: On types of trochilids in the Natural History Museum, Tring III. Amazilia alfaroana Underwood (1896), with notes on biogeography and geographical variation in the Saucerottia saucerrottei superspecies. Bulletin of the British Ornithologists’ Club 121(2): 98-107. 2001  Guy M. Kirwan; Nigel J. Collar: The ‘foremost ornithological mystery of Costa Rica’: Amazilia alfaroana Underwood, 1896. Zootaxa 4189(2): 244-250. 2016
The enigmatic Flame-rumped Sapphire was described in 1881, it is thought to originate from Brazil, however, according to the original description it doesn’t.:
“This is also one of Mr. Whitely’s recent discoveries, he having found it in company with a number of well-known Ecuador species of Humming- and other birds; so that it is reasonable to suppose it came from that country.” 
The Flame-rumped Sapphire might well be an now extinct species, however, it is now widely believed to be a hybrid of two other hummingbird species, the Glittering-bellied Emerald (Chlorostilbon lucidus (Shaw)) and the White-chinned Sapphire (Hylocharis cyanus Vieillot); I have included it here for the sake of completeness.
 Osbert Salvin; F. D. Godman: On some new and little-known species of Trochilidae. The Ibis 4(5): 595-597. 1881
Originally, Brace’s Emerald was only ever known by a single male specimen that had been collected in 1877 on the island of New Providence, Bahamas; this was long ignored completely and was considered identical with the Cuban Emerald (Chlorostilbon ricordii (Gervais)) which also inhabits the Bahamas. In 1945 it was then considered to be a subspecies of the Cuban Emerald; only in 1987 it was recognized as having been a completely distinct species.
Brace’s Emerald is now also known from fossil bones that were recovered from Pleistocene deposits on New Providence in the 1980s; it is now understood as a Pleistocene relict that had survived into modern times only to disappear completely after its discovery.
 Gary R. Graves; Storrs L. Olson: Chlorostilbon bracei Lawrence, an extinct species of hummingbird from new Providence Island, Bahamas. The Auk 104: 296-302. 1987
Letitia’s Thorntail, also known as Coppery Thorntail, was described in 1852, it is known only by two old male specimens (according to other sources by three specimens).
The species was for some time believed to represent a hybrid or a aberration of another species, the Raquet-tailed Coquette (Discosura longicaudus Gmelin) but was shown in a study in 1999 to be a valid species.
The origin of the Coppery Thorntail is not known, however, it is thought to have inhabited a region in northern Bolivia that even today has not been properly surveyed ornithologically.
Letitia’s Thorntail might be extinct, but there is a slight chance that it still survives in very small numbers.
This hummingbird form is known only by some ‘Bogota specimens’, that means by specimens that reached Europe via the bird markets of Bogota in Colombia, whose originin, however, remains obscure.
I the case of Travie’s Inca, which is also known as Lilac-fronted- or Lilac-spotted Starfrontlet, this form might actually be a hybrid of the Buff-winged Starfrontlet (Coeligena lutetiae (Delattre & Bourcier)) and the Collared Inka (Coeligena torquata (Boissonneau)).
However, since this form repeatedly appears in listings of extinct species, it will be mentioned here as well.