[ShiftIt][1] is a free app that does a similar job to some of the others mentioned here: CMD + ALT + CTRL + F gives you full-screen.  It also does quarter screen, center, and move to next screen if you have multiple monitors. It requires [XQuartz][2] which does rather dwarf its <1Mb download. Hadn't come across Spectacle before; it may offer a more complete feature set.

To address another issue mentioned: the accessibility options are under Preferences/Security and Privacy/Accessibility, not the top-level accessibility.


  [1]: https://github.com/fikovnik/ShiftIt
  [2]: http://xquartz.macosforge.org/landing/