Edited and improved! Now with pictures!
I like airplanes. Since there's a "Five Airplanes" meme going around, I'm powerless to resist it. So, here are my five picks.
They're not in any order, though. There's a pure fighter, an attack jet, a piston-powered attack plane, a medium transport, and a light taildragger, so they all served a distinct purpose, and as such would be hard to measure up against each other in a "better than" contest. They're also largely planes that hardly ever make a "Top Five" list, except for the first one on the list.
The sexiest fighter ever is the Supermarine Spitfire. There can be no argument about this; anyone who doesn't think that the Spitfire is to fighter aircraft what the Mona Lisa is to paintings simply has all of their taste in their mouth. It also had the capabilities to match its looks, which made it a supermodel with a punch. Fast, extremely maneuverable, and eminently adaptable, the various evolutions of the Spitfire were always at the top of the heap of piston-powered fighters in WWII, and with a good pilot behind the funny little ring-shaped stick, more than a match for anything the Jerries and Japs could put into the sky.
Douglas A-4 Skyhawk
The little attack jet known as the "Scooter" or "Bantam Bomber" hardly ever makes any "Top Ten" lists, but it's one of those designs they got just right for the intended purpose. Small, simple, agile, and robust, the A-4 was much loved by its pilots. A quarter the cost of an F-4 Phantom II, and with a wingspan so small that folding wings were not required for carrier use, the A-4 is a lot of capability in a well-engineered and balanced little package. A Skyhawk was the first jet airplane model I ever put together as a wee lad, and I've had an affinity for the A-4 ever since.
Sure, it's slow and lumbering, it doesn't carry bombs, and it can't shoot down enemy fighters, but the DC-3 brought the bullets and the other stuff necessary for fighting a war. The hero of the early airlines, the DC-3 was the first passenger plane to make a profit on passengers alone. The DC-3 revolutionized air travel in the 1930s, and it delivered the goods for the proper Hitler-and-Tojo ass-kicking less than a decade later. The old "Gooney Bird" may not be sexy, but she's a great aircraft by any definition of the term.
Piper J-3 Cub
The Model T of aviation, the little taildragger served as a trainer for more pilots than any other aircraft. Clad in olive drab paint, it served with distinction as a messenger, reconnaissance, and light transport plane in WWII. The Cub's STOL capabilities are unmatched, and there's simply no better fixed-wing airplane for flying in the weeds. Cubs soldier on as pleasure aircraft, and there's still a remarkable number of them delivering the goods up in Alaska, where its STOL capabilities make it popular with bush pilots.
Grumman G-21 "Goose"
The Grumman G-21 started out intended as a "flying yacht" commuter plane for wealthy Long Island businessmen in the 1930s. World War II intervened, and the little seaplane was put to use as a naval patrol and SAR plane. In British service, it acquired its nickname "Goose". The G-21 can haul a fair bit of cargo almost anywhere, not being constrained by availability of airstrips, and many ex-military Gooses were happily snatched up by civilian operators, especially in Alaska and Canada. The Goose is a sturdy "land anywhere" utility plane that has no equal to this day when it comes to sheer fuctionality.
Those are my picks. They are, of course, entirely subjective, but I tried to think of the kind of airplane that was simply a superior tool for the job at hand at the time, not just the best-looking one.