ShiftIt is a free app that does a similar job to some of the others mentioned here: CMD + ALT + CTRL + FCmd+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 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.