In the US, Google Account owners must be over 13, in the Netherlands it's 16 . It's common to lie to get accounts for younger kids, but this can cause an account lockout and 30 day deletion. 
So how do kids under 13 get personal email? All services have similar rules.
The exception, of course, is Google Apps for Education. They provide Google services, including calendar and email for children of all ages. The trick is that this group is excluded from Google's predatory business model ; the services are paid for and the school district assumes liability.
Is there something similar that's available outside of Education?
Well, there are Google Apps for Business (and on-profits) of course. I was unable to find any age requirements for businesses that buy Google Apps for Business, nor any requirement that the business had to be, you know, a real business. Google isolates business data from its ads and data mining so I expect US laws on protection of children from being packaged and sold do not apply.
At $50/user a year though, Google Apps for Business is a bit dear for a family of 5 (though the phone support is no little thing).
Unfortunately Google Apps for Nonprofits is not an option; you really do have to be a legal nonprofit.
Six years ago our family grandfathered into Google Apps through the now-defunct free option, and those users have since acquired full range of Google Services . Alas, that's not an option any longer.
I think the cheapest legal option is to sign up with a hosting service that provides Google Apps for your registered domain. I can personally recommend Dreamhost for this, based on my 6+ years of experience and the (unusual) fact that they handle Domain registration for their customers .
At approximately $100/year ($50 for first year or $97 for two years if you use my code ) Dreamhost's Google Apps service for a family of five is less than half the cost of Google Apps for Business -- albeit without phone support. On the other hand, Dreamhost also provides other web services including web hosting, Wordpress (ex. kateva.org/sh), web apps, etc .
There are other hosting services that provide Google Apps for potential family use, but Dreamhost is the one I know.
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 YouTube has an 18+ requirement for some videos, and Google Wallet is 18+. I don't believe either one is practically enforcable on most devices; maybe on Android or Chromebook depending on parental controls.
 It is noteworthy that Google's requirements for reversing account lockout are much more robust than their account recovery options. This says something about the power of laws and what Google could do to manage identity if they were forced to. The effective workaround is that a parent authorizes a credit card transaction on their own account, thereby technically committing fraud and assuming liability. The liability assumption is what matters.
 It's not that Google is particularly evil, this outcome is an inevitable outcome of their business model. They can no more resist this outcome than a species can resist Natural Selection.
 Not G+ though. It was once 18+ and is now 13+ regardless of Google Apps.
 Most hosting services have another party handle domain registration, and many of those deliver poor service.
 Admittedly more of a specialized interest these days.
 Just enter KATEVA when asked for a registration code. I set it up so users get the maximal $50/97 discount; I get a kickback but I set my kickback to maximize the user discount. Dreamhost supports Google's mutlifactor authentication framework, so I authenticate using Authenticator.app on my iPhone.