Zoo Keeper by Taito America, released in 1982 in the arcade.
Zoo Keeper - the original arcade, not the Nintendo DS version which is a Bejeweled knock-off. This game released on the cusp of the great Video Game Crash, and that probably is the reason I'd never seen nor heard of it until about 25 years later!
A very strange (but enjoyable) game, the main mechanic involves a character who must "build" confining walls to prevent animals from escaping a zoo. Walls are built by running in a rectangular pattern around on a screen, and your character is "bound" to this rectangular rail. As you reach an edge, his orientation will change (such that when you run on the underside of the bix, you are literally running "underneath" and the controls adjust accordingly). It's an odd setup, but fun to play and very unique. Meanwhile, animals trapped inside the walls are slowly eating their way out, so you must keep running to rebuild.
You can pick up a net (similar to Mario's Mallet or Pac-Man's energizer) for brief empowerment and temporarily have an offensive ability to thwart your enemies - otherwise, it's all running, jumping and dodging. Additionally, two Donkey Kong-inspired bonus stages liven up the gameplay.
Zoo Keeper is an eccentric older game, which never got a chance to thrive on home consoles (though a preproduction 2600 version was in progress). The game did well in the arcades, but the crash sealed its fate. Here is a very interesting account of the game's development, as told by the main programmer.