USS Midway - The Midway class was to be the next USN carrier class after the Essex clas, but WW2 ended befor eclass leader Midway could participate. As a consequence only 3 were built. USS Midway was the first USN carrier that was able to span from propellor-driven planes to modern jets. Some previous Essex class CVs were adequate into the mid-late 60s, but the Midways were able to serve into the 1990s.
USS Franklin - Member of the mighty Essex class that overwhelmed the Japanese Navy like a Tsunami. Franklin survived a devastating Kamikaze hit,
http://www.hazegray.org/danfs/carriers/cv13.htmAkagi - Akagi was being built as a battlecruiser, but the London Naval Treaty ended the building of new battleships and battle cruisers (because they start wars, doncha know). The treaty permitted converting some battle cruisers and battleships that were under construction to aircraft carriers. So Akagi and sister Amagi were converted ... well, not Amagi, as her hull was extensively damaged by an earthquake, so partly-built battleship Kaga was converted instead. The big points of significance of Akagi are that she and sister Kaga were where IJN carrier doctrine, from facilities layout to plane handling to squadron organization and fight doctrine were developed, and Akagi was one of six IJN carriers that carried out the Pearl Harbor attack.
HMS Hermes - The USN had the Midway, which served in the Gulf War, and the RN had the Hermes, which took the RN into the jet age and served in the Falklands War. More on this point amd more broadly below.
USS Enterprise (CV-6) - The Yorktown class (Yorktown, Enterprise, and Hornet) was the USN's first fully successful class of purpose-built fleet carriers. Yorktown fought at Coral Sea and Midway. Hornet launched the Doolittle Raid and then fought at Midway and in the early Solomons Campaign. The oft-wounded USS Enterprise fought just about everywhere in the Pacific, including surviving a devastating Kamikaze hit. Near perfect for WW2 in the Pacific, she was not adaptable to the jet age.
From my perspective, the history of aircraft carriers is too short with too many equally significant parallel paths to suit a Top 5
list format. My Top-5-ish approach would be thus:
Experimental carriers - RN HMS Argus, USN USS Langley, IJN Hosho. These were the beginning of the development of the aircraft carrier concept. How could one say that any one of these was more significant?
Treaty-forced conversions - RN Courageous class (converted from battle cruiser), USN Lexington class (converted from battle cruiser); IJN Akagi and Kaga, French Navy Bearn (converted from battleship). These were the ships on which their respective navies took a proven concept into formidable fighting ships.
First fully successful purpose-built fleet carriers - RN HMS Ark Royal, USN Yorktown class, IJN Shokaku class. These became the backbones of their respective navies' carrier fleets in WW2. Enterprise, Shokaku, and Zuikaku fought in most of the whole war in the Pacific.
Early jet age carriers - RN Audacious and Centaur classes, USN Essex, Midway, and Forrestal classes, French navy Clemenceau class. Going from propellors to jets and helicopters. Some Essex class carriers were tasked to recover astronauts and capsules for NASA; some fought in the Vietnam War. HMS Hermes, as noted above, fought in the Falklands War, and USS Midway in the Gulf War.
USS Enterprise, CVN-65 - the USN's first nuclear powered carrier and forebear of the Nimitz class. Her years of active service spanned from 1961 into 2012, and she was decommissioned in 2017.