So... With Android, you need to use a gmail account for the Play store, a Live account if you've picked a windows phone, or an itunes account if you've gone with an iphone. If you're that concerned, you would need to either not download apps, or get a "dumb" phone.
NOW, the other option, would be to install a secondary market, such as the Amazon appstore, GetJar, or any other legit store. It's nice that Android lets you pick huh?
No, you're all sorts of confused.
First of all, it's called a Microsoft Account, and you can use a non-Outlook.com email to set up a Microsoft Account. Microsoft has the necessary fields to set which email addresses to send all notifications to, as well. Google doesn't have this.
Secondly, you can use any email address to set up an Apple ID.
The issue is less of the Gmail requirement and more of the inability to Delete Gmail and get your stuff to go to a different email address. AFAIK, Google Play Store - unlike iTunes/App Store and Microsoft/Windows Store doesn't give you the choice on where to get this stuff sent. A ton of Google services default to this Gmail address and don't give you an option of where to send this stuff.
This is different from Microsoft and Apple, and it's also different form companies like RIM/Blackberry and Yahoo! who allow you to set any email address as your Blackberry ID (similar to iTunes) or Log-In/Use a different email address for services they own, like Flickr (Flickr doesn't force you to use Yahoo! Mail to get notifications from them).
I've also been looking at a way to delete Gmail and still use Android (cause the iPhone is too narrow a keyboard for me to type on, and Windows Phone doesn't have apps I absolutely require), because as a Windows 8/Outlook 2013/IE 10 user Gmail/Google Talk is a pretty bad user experience and at this point the only use I have for that account is keeping my purchased apps functioning.
If anyone is brave enough, delete Gmail from your Google Account and try to get a Free Song of the Day or something, and see what happens...