OSX: "Minecraft quit unexpectedly" on launcher startup

This seems to be a common issue on Mac OS X 10.8.5 - Temporarily, you need to use the legacy launcher and have Java installed: http://launcher.mojang.com/download/Minecraft_legacy.dmg

Please be aware that Mac OS X 10.8 is no longer supported, the minimum requirement has risen to OS X 10.9: https://help.mojang.com/customer/portal/articles/325948