“Not only should your apps stop relying on the hardware Menu button, but you should stop thinking about your activities using a [menu button' at all,” Scott Main, lead tech writer for developer.android.com, stated in a blog post. “Your activities should provide buttons for important user actions directly in the action bar (or elsewhere on screen). Those that can’t fit in the action bar end up in the action overflow.”
Main says that even if an app is built to support versions of Android older than 3.0, there's no Menu button on later builds. Instead, the button that appears at the bottom is a action overflow command for legacy apps. In other words, Google doesn't even want developers/users to use the term “Menu button” anymore.
“This might seem like splitting hairs over terminology, but the name action overflow promotes a different way of thinking,” Main explains. “Instead of thinking about a menu that serves as a catch-all for various user options, you should think more about which user options you want to display on the screen as actions. Those that don't need to be on the screen can overflow off the screen. Users can reveal the overflow and other options by touching an overflow button that appears alongside the on-screen action buttons.”
Android, of course, is an open source operating system that thrives on its community of developers, and there are mods available that bring the Menu button back, provided you're comfortable rooting your phone.