The Angels of Neon Genesis Evangelion are bizarre creatures that threaten to destroy humanity, and their powers and abilities can be pretty hard to understand at times. Here's a rundown of all 17 Angels that appear in the original series, what they're capable of, and when they show up.
Adam & Lilith
Adam and Lilith are the First and Second Angels, respectively. Adam was discovered in Antarctica, and its discovery caused the Second Impact. Adam is the progenitor of the Angels, a being sent to Earth to populate the planet with life back in its earliest days. Lilith is the progenitor of humanity and was discovered in Japan where the Geofront is located. Lilith is shown with a strange mask on its face, the design of which matches the logo of SEELE. The Evangelion units are all based on Adam, except for Unit 01, which is instead based on Lilith. Lilith first appears in episode 15, while Adam debuts in episode 8.
Sachiel
Sachiel is the Third Angel, and the first to appear after Second Impact occurs, in episode 1. Its humanoid form emerges from the Pacific Ocean and makes a beeline for Tokyo-3 and NERV HQ. It puts up a tough fight against Rei in Evangelion Unit 00, and is eventually defeated by Shinji in Unit 01. Sachiel featured bony protrusions from its arms and is capable of firing an intense energy beam. Sachiel was destroyed when it self-destructed in an unsuccessful attempt to take Unit 01 with it.
Shamshel
Shamshel is the Fourth Angel, appearing in episode 3. Shamshel has small legs and a long body, looking a bit like a dragonfly without wings. Shamshel fought ferociously against Evangelion Unit 01, and used several clever tricks, such as severing the power cord, to gain the upper hand. Shamshel could create energy whips out of its tiny arm-like appendages, which were capable of burning Unit 01's hands. Shamshel was destroyed when Shinji in Unit 01 stabbed its core.
Ramiel
Ramiel is the Fifth Angel, appropriately appearing in episode 5 of the series. Ramiel is one of the most well-known angels due to its bizarrely simplistic appearance: it's just a blue octahedron, a shape with 8 triangular faces. Ramiel's alien nature made it difficult to fight, as it had a strong AT Field, and it was equipped with a powerful energy beam that melted through Unit 00's shield. Ramiel was ultimately defeated by Shinji in EVA Unit 01, firing a super-powered rifle charged with Japan's entire electrical output, although Rei gets credit for the assist on this one.
Gaghiel
Gaghiel is the Sixth Angel and appears in Episode 8 for Asuka's debut. It resembles a whale-like creature and is depicted swimming through the waters around a fleet of warships. Gaghiel differs from prior angels in that most of its offensive capability was physical, relating to its shark-like teeth. It proved a challenge, as Evangelion Unit 02 was not equipped to fight underwater. It was finally destroyed when Shinji and Asuka, working together in Unit 02, held its mouth open long enough to get a few of the abandoned battleships inside and cause them to self-destruct, shattering the Angel's core.
Israfel
Israfel is the Seventh Angel, appearing in episode 9. It also has a vaguely humanoid form and emerged from the ocean. Israfel's greatest ability was the fact that it possessed not one, but two cores, and destroying one at a time wasn't sufficient. It could also divide itself into two slightly smaller bodies, with one core in each. They initially defeated Evangelion Units 01 and 02, and were only contained while repairs were made by dropping an atom bomb-tier explosive on them. Shinji and Asuka had to train to synchronize their movements in order to defeat it by piercing both cores simultaneously.
Sandalphon
Sandalphon is the Eighth Angel, appearing in episode 10. Although first discovered while still in the embryonic state, Sandalphon's hatched form resembles a primordial deep sea creature. NERV wanted to get the jump on Sandalphon, but it was incubating deep within a volcano, making it difficult to reach. Using special equipment, Asuka in Unit 02 had to dive into the magma to attempt to destroy it before it could hatch, but fails. Asuka is eventually able to destroy it using a Progressive Knife from Shinji. Since it was still young, it's unknown what its full capabilities would have been.
Matarael
Matarael is the Ninth Angel, appearing in episode 11. It has a small central body supported by long, spider-like legs, which are covered in triangles with eyes resembling the Eye of Providence. Matarael attacked Tokyo-3 while the city was in a state of blackout, making it impossible to detect initially. Matarael was shown attacking with acid, which it used to keep the Evangelions from climbing out of the launch tubes. It was defeated by Shinji, Rei, and Asuka working together, as Asuka took down its AT Field and Rei retrieved the lost Pallet Rifle for Shinji, who delivered the killing blow.
Sahaquiel
Sahaquiel is the Tenth Angel, appearing in episode 12. Sahaquiel has a bizarre appearance, its central body is a large eye with two strangely shaped arms/wings protruding from either side. It appeared from space and began dropping explosive pieces of itself from orbit, dealing massive damage anywhere they landed. It also proved immune to the atomic-tier N2 bombs thanks to a powerful AT Field. It was defeated by the trio of Evangelion pilots working together once again, with Asuka landing the killing blow this time with a Progressive Knife.
Ireul
Ireul is the Eleventh Angel, appearing in episode 13. Unlike all the others, which were massive creatures, Ireul is a microscopic, virus-like organism. It first appeared within the Geofront, causing a strange form of corrosion to spread across everything that it touched. It attempted to cause the base to self-destruct, but Ritsuko was able to thwart it using the last uncorrupted MAGI computer. Due to its size, it never went up against an Evangelion.
Leliel
Leliel is the Twelfth Angel, and appears in episode 16. It was a being that existed in greater than 3 dimensions, and manifested in the world as a shadow, seemingly cast by a floating sphere above it when in fact the opposite was true. As one of the most bizarre Angels, it was incredibly difficult to fight, and it absorbed Unit 01 into its extradimensional space. Leliel was destroyed when Unit 01 went berserk while inside, shredding the creature just before a torrent of bombs is about to be dropped on it.
Bardiel
Bardiel is the Thirteenth Angel, appearing in episode 18. Bardiel's true form isn't seen but is implied to have been small, as it was able to hide in the clouds and hijack Unit 03 as it passed by. Bardiel grew within Unit 03 and turned it into an angel, despite the Evangelion's pilot, Toji Suzuhara, still being inside. Unit 01 is deployed to fight it, but Shinji refuses due to Toji's presence; control of Unit 01 is turned over to the dummy system, which violently crushes Unit 03's entry plug, killing Bardiel and horribly injuring Toji.
Zeruel
Zeruel, the Fourteenth Angel, appears in episode 19. It, too, has a humanoid form, although arguably less human than Sachiel or Israfel. It was exceptionally strong and managed a major incursion into the Geofront through its attack. Its "arms" are paper-thin, giving them incredible slicing power. It could levitate, and fired energy beams from its eyes which were absurdly powerful. It is eventually destroyed by Unit 01, and the "S2 Engine" within Zeruel was devoured by Unit 01, drastically increasing the EVA's power.
Arael
Arael, the Fifteenth Angel, appears in episode 22. It's another strange one, with a largely incorporeal body made of light, and it attacked by using its AT field to make telepathic contact with the EVA pilots and forcing them to relive traumatic memories. Like Sahaquiel, it approached from space, which made it a challenge to fight. It's defeated by Rei using the Lance of Longinus, which she catapults into orbit; the Lance is then lost in space afterward.
Armisael
Armisael, the Sixteenth Angel, appears in episode 23. Its body takes the shape of a double helix made of light, which initially wraps around so that the two ends touch, forming a circle. It was also able to psychically interact with the EVA pilots, and managed to bond itself to Rei in Unit 00, causing her to feel its pain, and nearly took Unit 01 as well. Rei decides to self-destruct Unit 00, destroying Armisael along with a huge chunk of Tokyo-3.
Tabris
Tabris, the Seventeeth Angel, is better known to Evangelion fans as Kaworu Nagisa, and appears in episode 24. Kaworu isn't a "natural" angel, but rather a being created by SEELE as a vessel for Adam's soul, making him similar to Rei in many ways. He is the Fifth Child, and is sent in disguise as a human to replace Asuka as the pilot of Unit 02. Kaworu and Shinji quickly develop a close relationship, but Kaworu eventually tries to descend to Terminal Dogma and join with Adam, only to find Lilith, not Adam. Having failed, Kaworu gives permission to Shinji to kill him, and dies when crushed by Unit 01's hands.