Donkey Kong 3 often catches some flak for being a great departure from the first two Donkey Kongs, being a shooter instead of a platformer. To which I say, so what? It's a really, really good shooter!
The first interesting thing about the game is its setting. The vast majority of fixed-shooter arcade games were set in space, and had you battling aliens, but DK3 is instead set in the deep jungle. Stanley the Bugman (Mario is MIA) must shoot down an army of menacing bugs, who are trying to steal his flowers. There's a lot of strategy involved, as Stanley can only shoot upwards, so he must constantly shift around and about the 3-story structure he's on, in order to be able to hit the enemies.
Like the last two games, Donkey Kong is a constant presence at the top of the screen, and he is the one that sends down the obstacles. However, unlike Donkey Kong and Donkey Kong Jr., this time around he can be interacted with, and indeed, doing so is the only way to complete a stage. You have to shoot at his rear end, sending him upwards, until he reaches the top of the screen and gets knocked out. This provides a lot of the games charming humor: DK has a hilarious look on his face as he gets shot in the butt, and there's always a comedic misfortune waiting for him at the top (such as a beehive that gets dropped on his head!).
Donkey Kong 3 isn't really considered a classic arcade game, but I think it ought to be. It's an endlessly fun shoot-em-up, with a lot of replay value (gotta get that high score!), and if nothing else, it's noteworthy as being the last Mario-related arcade game, before the series got a tune-up with the NES legend Super Mario Bros.