There are about 9,993 living species of birds known by scientists. A collaboration between scientists at Yale and the Zoological Society of London (ZSL) have analyzed all of them and determined the world’s avian biodiversity.  This is part of ZSL’s Evolutionary Distinct and Globally Endangered (EDGE) species list, and they have ranked 100 bird species based on conservation status and how unusual they are compared to other birds.
The list includes representatives from 20 of the 29 known orders. The birds are declining in population for a variety of reasons, though poaching, habitat destruction, and introduced predators are the most common threats.
The top 15 are listed here with details and pictures, and the rest of the list follows below:
1. Giant Ibis (Thaumatibis Gigantea)
Image credit: Henrick Grönvold
The Giant Ibis is critically endangered, with only about 230 mating pairs left in the wild. Most surviving members live in Cambodia, though there are a few living in Laos and Vietnam. This is the largest of the ibises, measuring up to 100 cm (39 in) tall and weighing up to 4.2 kg (9.3 lbs). 
2. New Caledonian Owlet-nightjar (Aegotheles savesi)
Image credit: Joseph Smidt
The conservation status of this bird, which is endemic to New Caledonia, isn’t well known. It is believed that there are probably less than 50 individuals remaining, but scientists haven’t seen any of this species since 1998, which is the only sighting since 1960. 
3. California Condor (Gymnogyps californianus)
Image credit: Stacy via WikiMedia Commons
In 1987, there were so few California Condors that all 21 remaining individuals were collected and the species was declared extinct in the wild. Through dedicated breeding programs, the birds were reintroduced into protected areas in 1991. There are now over 237 living in the wild. These huge birds have a 3 m (9.8 ft) wingspan and weigh up to 12 kg (26 lbs)
4. Kakapo (Strigops habroptila)
Image credit: Mnolf via WikiMedia Commons
This nocturnal flightless bird, endemic to New Zealand, is critically endangered with only 130 wild individuals remaining. The kakapo is the heaviest species of parrot, weighing up to 4 kg (9 lbs) when it reaches adulthood. 
5. Kagu (Rhynochetos jubatus)
Image credit: Scott Meyer
The Kagu is endemic to New Caledonia and has a structure that is only found in members of this species: nasal corns. This is a structure which covers the nostrils, which is believed to shield dirt from entering the nostrils when the bird digs for insects.
6. Bengal Florican (Houbaropsis bengalensis)
Image credit: Richard Leydekker
There are likely fewer than 500 adults remaining of this species, which live in isolated populations in India and Southeast Asia. This species is the most threatened of all bustards, which are large terrestrial birds. Bengal Floricans grow up to 68 cm (27 in) in height and weigh up to 1.9 kg (4.2 lbs).
7. Forest Owlet (Heteroglaux blewitti)
Image credit: Dr. Raju Kasambe
This owl is endemic to India and was first believed to be extinct in 1884. A small population was discovered in 1997 and only 25 birds have been located since 2000, though it is estimated that there could be as many as 250 individuals remaining.
8. Philippine Eagle (Pithecophaga jefferyi)
Image credit: Harry Balais
This eagle is endemic to the Philippines and grows to an incredible 102 cm (3.4 ft) tall and can weigh up to 8 kg (17.6 lbs). Its crest of feathers resembles the mythical griffin, which is part lion, part eagle. Estimates on the number of breeding pairs varies, and could be as few as 82 or as many as 233 (which really isn’t that many).
9. Christmas Island Frigatebird (Fregata andrewsi)
Image credit: Shah Jahan
This bird is endemic to the Christmas Island, Australia. Its top predator is the yellow crazy ant, which was inadvertently introduced via trade ships. The ants attack the birds during breeding season.
10. Sumatran Ground-cuckoo (Carpococcyx viridis)
This bird is endemic to Sumatra and can grow up to 55 cm (22 in) in length. There are estimated to be fewer than 250 individuals left. Over a 90 year period, the bird has only been spotted twice; most recently from a tiger camera trap in 2006, though its call was identified in 2007.
11. Spoon-billed Sandpiper
12. Northern Bald Ibis
13. Plains-wanderer
14. New Zealand Storm-petrel
15. Hooded Grebe
16. White-shouldered Ibis
17. Maleo
18. Black-hooded Coucal
19. Madagascar Serpent-eagle
20. Dwarf Olive Ibis
21. Rufous Scrub-bird
22. Noisy Scrub-bird
23. Junin Grebe
24. White-collared Kite
25. Congo Bay-owl
26. White-eyed River-martin
27. Red-headed Vulture
28. Secretarybird
29. Peruvian Diving-petrel
30. Egyptian Vulture
31. St Helena Plover
32. Australian Painted Snipe
33. Cuban Kite
34. Tooth-billed Pigeon
35. Nahan's Francolin
36. Sulu Hornbill
37. Shoebill
38. Purple-winged Ground-dove
39. Asian Crested Ibis
40. Sangihe Shrike-thrush
41. Jerdon's Courser
42. Lesser Florican
43. Kokako
44. Rufous-headed Hornbill
45. Masked Finfoot
46. Bahia Tapaculo
47. Waved Albatross
48. Stresemann's Bristlefront
49. Sociable Lapwing
50. Eskimo Curlew
51. Slender-billed Curlew
52. Bannerman's Turaco
53. Ashy Storm-petrel
54. Siberian Crane
55. White-throated Storm-petrel
56. Juan Fernandez Firecrown
57. Dark-winged Trumpeter
58. Uluguru Bush-shrike
59. Polynesian Ground-dove
60. Sichuan Jay
61. Mountain Serpent-eagle
62. Sulu Bleeding-heart
63. Zapata Rail
64. Mindoro Bleeding-heart
65. Kaka
66. Negros Bleeding-heart
67. Black Stilt
68. Makira Moorhen
69. Great Indian Bustard
70. Abbott's Booby
71. Kittlitz's Murrelet
72. Titicaca Grebe
73. Greater Adjutant
74. Western Bristlebird
75. Eastern Bristlebird
76. Shore Plover
77. Udzungwa Forest-partridge
78. Madagascar Fish-eagle
79. White-bellied Heron
80. Subdesert Mesite
81. Long-whiskered Owlet
82. Philippine Cockatoo
83. Spix's Macaw
84. South Island Wren
85. Crow Honeyeater
86. Northern Brown Kiwi
87. Banded Ground-cuckoo
88. Flores Hawk-eagle
89. Tachira Antpitta
90. Beck's Petrel
91. Cebu Flowerpecker
92. Blue-eyed Ground-dove
93. Javan Trogon
94. Pulitzer's Longbill
95. Alagoas Antwren
96. Pernambuco Pygmy-owl
97. Jamaica Petrel
98. Grenada Dove
99. Wood Snipe
100. Rio de Janeiro Antwren