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First, let me introduce you to a beautiful framework to be aware of as you read the list below of alternatives to Google's functions. It's Cal Newport's divide-and-conquor approach to handeling Social Media and other technologies described in his newest book Digital Minimalism (2019). He lays out a plan to reboot your digital life according to your values in three steps:

The Digital Declutter

1. Define specific technology rules for a 30 day period, where you stop using "optional technologies".

1. Take the 30 day break from optional technologies and follow the rules

1. Reintroduce selected technologies

This recipe should help you use digital technology to serve your needs. However, to avoid overuse, distraction and wasted time, he suggests a stringent set of criteria for which technologies to reintroduce. Here they are verbatim (p. 77): 

The Minimalist Technology Screen

To allow an optional technology back into your life at the end of the digitial declutter, it must:

1. Serve something you deeply value (offering some value is not enough)

1. Be the best way to use technology to serve this value (if it's not, replace it with something better)

1. Have a role in your life that is constrained with a standard operating procedure that specifies when and how you use it

Regardless of whether you try Newport's digital declutter, you can immediately stop using or replace certain technologies today, if you sense they are not the best way of serving your values. With this in mind,  know that Facebook wants you to think binarily: Either you use Facebook or you don't. 

This allows the to entice you into their ecosystem with some feature you find important, and then, once you're a "user", deploy attention engineering to overwhelm you with integrated options, trying to keep you engaging with their service well beyond your original purpose

- Digital Minimalism, p. 76 

But you don't have to fall for that. Google is a conglomeration of different functions, which you use to different degrees and that you can use or stop using consciously. With this in mind, it can be useful to know alternatives to specific functions. 

This list consists of my own research, but is mainly copied from Restore Privacy's guide to Google alternatives. I also found Wired's guide to the ways Google tracks us and how to opt out highly informative.

Gmail

Google Search

• Searx – A very privacy-friendly and versatile metasearch engine.
• Qwant – A private search engine based in France.
• DuckDuckGo – This is a great privacy-friendly Google alternative that doesn’t utilize tracking or targeted ads. They also have a zero-sharing policy with other features, but they do record search terms.
• StartPage – StartPage gives you Google search results, but without the tracking.
• Metager – A private search engine based in Germany.

(From Restore Privacy)

Other nice search engines:

• Ecosia - plants trees with the profit from adds
• WolframAlpha - mathematical search engine
• Disconnect Search - Searches privately via your favorite search engines.

Google Maps

Peter's liste:

• Krak.dk 
• Apple Maps via duckduckgo.com
• Maps.me
• Kortforsyningen

A map alternative for PCs isOpenStreetMap.

A few Google Maps alternatives for mobile devices include:

• OsmAnd is a free and open-source mobile maps app for both Android and iOS (based on OpenStreetMap data).
• Maps (F Droid) uses OpenStreetMap data (offline).
• Here WeGo provides good mapping solutions for both PCs and mobile devices with their app.
• Maps.Me is another option that is free on both Android and iOS, but there is a fair amount of data collection with this alternative, as explained in their privacy policy.
• MapHub is also based on OpenStreeMap data and it does not collect locations or user IP addresses.

Note: Waze is not an “alternative” as it is now owned by Google.

Google Chrome (browser)

• Firefox browser – Firefox is a very customizable, open-source browser that is popular in privacy circles. There are also many different Firefox modifications and tweaks that will give you more privacy and security. (Also check out Firefox Focus, a privacy-focused version for mobile users.)
  
• Firefox privacy on Restore Privacy. 
  
• Transfering data from Chrome to Firefox

Google Drive

I personally use Mailbox.org and pay for extra cloud storage, which is then integrated with my email. 

• Tresorit – A user-friendly cloud storage option based in Switzerland.
• ownCloud – An open source and self-hosted cloud platform developed in Germany.
• Nextcloud – Nextcloud is also an open source, self-hosted file sharing and collaboration platform, based in Germany.
• Sync – Based in Canada, Sync offers a secure, encrypted cloud storage solution for businesses and individuals.
• Syncthing – Here we have a decentralized, open source, peer-to-peer cloud storage platform.

Of course, Dropbox is another popular Google drive alternative, but it’s not the best in terms of privacy.

Google Calendar

Here are some Google Calendar alternatives:

• Lightening Calendar is an open source calendar option developed by Mozilla, and it’s compatible with Thunderbird and Seamonkey.
• Etar, an open source, basic calendar option.
• Fruux, an open source calendar with good features and support for many operating systems.

For those wanting a combined solution for both email and calendar functionality, these providers offer that:

• Mailfence
• Kolab Now
• Posteo.de
• Mailbox.org
• Tutanota

Google Docs / Sheets / Slides alternative

There are many solid Google Docs alternatives available. The largest offline document editing suite is, of course, Microsoft Office. As most people know, however, Microsoft is not the best company for privacy. Nonetheless, there are a few other good Google Docs alternatives:

• CryptPad – CryptPad is a privacy-focused alternative with strong encryption, and it’s free.
• Etherpad – A self-hosted collaborative online editor that’s also open source.
• Mailfence Documents – From the Mailfence team, this is a secure file sharing, storage, and collaboration tool.
• Zoho Docs – This is another good Google Docs alternative with a clean interface and good functionality, although it may not be the best for privacy.
• OnlyOffice – OnlyOffice feels a bit more restricted than some of the other options in terms of features.
• Cryptee – This is a privacy-focused platform for photo and document storage and editing. It’s open source and based in Estonia.
• LibreOffice (offline) – You can use LibreOffice which is free and open source.
• Apache OpenOffice (offline) – Another good open source office suite.

Google Photos alternative

Here are a few good Google Photos alternatives:

• Piwigo – Piwigo is a great option that you can self-host. It is also free and open source.
• Lychee – Lychee is another self-hosted, open source photo management platform.
• Cryptee – Mentioned already above, Cyrptee is also a great option for securely storing photos.

Shoebox was another alternative, but it closed operations in June 2019.

YouTube alternatives

Unfortunately, YouTube alternatives can really be hit or miss, with most struggling to gain popularity.

• Peertube
• DTube
• Bitchute
• invidio.us
• Vimeo
• Bit.tube
• Dailymotion
• Hooktube

Tip: Invidio.us is a great Youtube proxy that allows you to watch any Youtube video without logging in, even if the video is somehow restricted. To do this, simply replace [www.youtube.com] with [invidio.us] in the URL you want to view.

Google translate alternative

Here are a few Google translate alternatives I have come across:

• DeepL – DeepL is a solid Google Translate alternative that seems to give great results. Like Google Translate, DeepL allows you to post up to 5,000 characters at a time (but the pro version is unlimited). The user interface is good and there is also a built-in dictionary feature.
• Linguee – Linguee does not allow you to post large blocks of text like DeepL. However, Linguee will give you very accurate translations for single words or phrases, along with context examples.
• dict.cc – This Google Translate alternative seems to do a decent job on single-world lookups, but it also feels a bit outdated.
• Swisscows Translate – A good translation service supporting many languages.

If you want to translate blocks of text, check out DeepL. If you want in-depth translations for single words or phrases, then Linguee is a good choice.

Google Keep (Notes)

• Standard Notes is a great alternative for a note-taking service. It is secure, encrypted, and free with apps for Windows, Mac, Linux, iOS, and Android (web-based also available).
• Joplin is another great option that is open source and works on Windows, Mac, Linux, iOS, and Android.

Google analytics alternative

For website admins, there are many reasons to use an alternative to Google analytics. Aside from privacy concerns, there are also faster and more user-friendly alternatives that also respect your visitors’ privacy.

• Clicky is a great alternative to Google Analytics that truncates and anonymizes visitor IP addresses by default. It is lightweight, user-friendly, and fully compliant with GDPR regulations, while also being certified by Privacy Shield.
• Matomo (formerly Piwik) is an open-source analytics platform that respects the privacy of visitors by anonymizing and truncating visitor IP addresses (if enabled by the website admin). It is also certified to respect user privacy.
• Fathom Analytics is an open source alternative to Google Analytics that’s available on Github here. It’s minimal, fast, and lightweight.
• Get Insights – Another privacy-focused analytics platform, with a full analytics suite. The front-end client is open source and available here.
• AT Internet is a France-based analytics provider that is fully GDPR compliant, with all data stored on French servers, and a good track record going back to 1996.

Many websites host Google Analytics because they run Google Adsense campaigns. Without Google Analytics, tracking performance of these campaigns would be difficult. Nonetheless, there are still better options for privacy.