It is true that you can get Play Store apps without a Google Account, but the Place Services framework does a lot more than this. Many apps rely upon the framework for certain pieces of functionality from Google's libraries.
You mean Google Apps specifically?
I don't use them personally but I imagine Goole Now, GMail and Google Maps would need Play Services.
The apps I do use (non-google) tend to function well enough without Play Services though.
Re:A Message to Our Customers
by thelibrarian on Wednesday February 17, 2016 @04:22PM
(#11121518)
Many Android apps include the Google Play Services framework in themselves, as they provide extra functionality that is not in the baseline Android API, e.g. a JSON parser.
This isn't true. You can stick to app repositories like F-Droid and use Raccoon to download Play Store apps via your desktop without using a Google account on your phone.