Exit the Goolag 
For whatever reason you have decided it is time to remove yourself from the Google universe, below are the services I have used to extricate myself. Feel free to comment on alternatives or opinions on what could be done better.
Note that I receive no compensation from any service listed here.
This post has become the most popular one on this site, so I am expanding the instructions for each section to make it more approachable to the non-technical community of users that are realizing they need to make the move away from Google.
Mail, Calendar and Contacts
The center of most people’s online world is the email, calendar and contacts that Gmail provides. When exiting the Goolag I chose to use FastMail, an excellent service provider that offers the same suite of services and stellar web interface (which I believe is superior to Gmail), mobile apps and the ability to integrate into other applications that use IMAP, CalDAV and CardDAV (all open source standards). Since the original version of this I also added ProtonMail and find that an excellent provider as well.
This link below will cover how to move to a new email provider:
Move to a new email provider
Browser
The first application to replace is the Chrome web browser. The best two options are Firefox or Brave. [Note: due to the decision by Firefox to support censorship on the internet they can no longer be recommended or trusted.] Brave comes with extensive privacy options and importantly are not owned by Google.
Search Engine
The core of the Google efforts to spy on your privacy to sell your personal data to advertisers is their search engine. Personally I switched to Bing by Microsoft. Another option for people who want a purely non-corporate experience is DuckDuckGo.