Entanglement is the first video game I've played that looks like a bowl of spaghetti, though it plays more like a challenge to create the bendiest boulevard in Sim City or Civilization.
The game is a descendant of Pipe Mania, a puzzling challenge that has players laying out a circuitous route by applying pieces to a grid. The goal is to create a path through which a line of color can travel in a continuous flow. Entanglement lets players lay hexagons, each of which has a few possible pathways on it. Players can swap them or rotate them, extending and entangling their pathway. What starts as a simple winding lane for your orange dot become a nest that, ideally, is comprised of one elegant line.
In the video here, I'm playing the iPad version, Entanglement HD. Both iPhone ($2) and iPad ($4) versions are relatively simple but excellent time sinks. The web version is more fully-featured and can be tried for free (go here for the Chrome-optimized version of that one — or this one if you have any other browser).
Whatever your platform, try Entanglement if you need a new game to zone out to and if you don't mind suddenly seeing the words you're typing as a bunch of possible pathways for a winding line of color. I can't stop seeing paths!