page--front.tpl.php not showing up in Zen subtheme
Found out the problem was caused by the Context Layout module. Apparently this module overrides Drupal's normal template file search order. The solution was to either to disable the Context Layout module or include the templates (like page--front.tpl.php) in the layouts definition in the themename.info file. I went with the latter solution.

Here is an example of what should appear in the .info file:

; Layout: Landing 
layouts[landing][name] = "Landing Page"
layouts[landing][description] = "A layout for landing pages."
layouts[landing][template] = "templates/page--front"
layouts[landing][regions][] = "search"
layouts[landing][regions][] = "highlighted"
layouts[landing][regions][] = "mega_menu"
layouts[landing][regions][] = "slider"
layouts[landing][regions][] = "sidebar_first"
layouts[landing][regions][] = "sidebar_second"
layouts[landing][regions][] = "footer"
layouts[landing][regions][] = "bottom"


Notice the layouts[landing][template] line where we define where and what template file to use. This is key to getting this to work with Context Layouts.