I value a lot my privacy, much further than the mere act of adblocking half of the internet to avoid targeted advertisement and tracking. While my specific methods and tools evolve over time (although are still similar to those I wrote about in 2015), sometimes you get "vendor locked-in" and becomes hard to break free from those restrictions.
While I think Google is awesome as a technical company, they also worry me a lot because of the power to store, infer and correlate information about mostly everything. And for many years I've been using Google Apps for Domain and many of their services... They are generally great, convenient and powerful. But, at the same time, you feed more info and even leave private bits (emails, appointments, documents) inside them. And that was something I wasn't comfortable with.
So, a few months ago I decided to build a plan on how to cut my ties with GApps. This are the results and the services I use instead of Google's. There are "cheats" and I'm also restricted to use Linux so others using Windows or Mac will probably have better (paid) alternatives.
That said, let's go with the list:
GMail and mail Contacts: I'm a happy paying ProtonMail user. I exported all my old emails to Mozilla Thunderbird just in case I need to check something but I've decided to keep a "sliding window" of a few years of emails (I think is around 6) and wipe out older stuff.
GDrive: I decided to use Dropbox after getting tired of synchronization conflicts using Box, with a third-party sync script as there isn't even official Linux support. Dropbox Linux client works flawlessly.
Documents and spreadsheets: I combine Dropbox with LibreOffice. LibreOffice is painful to use (feels and works like a bad copy of MS Office 2000), but I haven't got anything better and don't want to need to boot up a VM with a proper MS Office inside for editing documents.
Keep/notes: I use Dropbox Paper, which is really nice on the desktop and works from mobile, although sometimes feels slow responding to typing.
Search: I've been using for years DuckDuckGo and don't miss at all Google's previously-incredible-but-now-increasingly-biased search results.
Presentations: Here I suffer, because despite not being great, Google Slides were a much better alternative than the terrible LibreOffice Impress. So I sometimes cheated and used my Google Apps account to create the slides, and now I just use a Windows VM with MS Powerpoint. Even a default template in PPTX already has conversion and visualization issues at LibreOffice.
Calendar: I didn't found anything fully satisfying so I built my own crappy alterantive, and being web-based, one app less to install and keep updated.
Hangouts: WhatsApp or Telegram, but if needs to be Hangouts there's no alternative but to use it (but only from a desktop browser).
Maps: Can't fully avoid it from mobile, but whenever possible I use CityMapper.
Youtube: Don't use it much and never from mobile, so I just watch whatever others send me being always logged out.
Google+: Only use I can think about this service is as a secret vault, as only Google employees use it and would read them. Bad jokes aside, Twitter is a much better alternative to share links and blog posts.
And then comes the big catch... What to do if you use an Android phone? Well... here basically you're screwed up. You have to keep using it, and somehow manually synchronizing your phone contacts (which are in fact GMail ones) with whatever system you use . This is the only real setback I have... I ended up using a different domain name for my new email, so the account is not even Google Apps enabled. I left the old one mostly to use the phone and redirect emails.
 In my case I just manually add new contacts to ProtonMail, so it doesn't gets full of clutter from people who wrote or called me just once (as happens with GMail).