Although primarily dealing in email hosting, FastMail also offers a few complimentary tools, including calendars. This makes FastMail a convenient choice if you want both.
For a less sophisticated, but cheaper alternative, Mailbox.org has a similar offering. If you are looking for an Android app, Etar makes a nice replacement.
The next most popular browser, but long time favourite of many, FireFox is a great browser, with some unique privacy features.
If you are looking for something closer to Chrome try Vivaldi, which supports Chrome extensions. Mac users have some additional options in Arc and Orion.
For cloud based text documents, Notion gives you most of what's convenient about Docs, with some nice added features. A good fit if you like writing in Markdown.
For something closer in design to Docs, take a look at Zoho Writer. Alternatively, Dropbox Paper falls somewhere between the two, being more business oriented.
A privacy and security focus, and a good amount of free storage makes pCloud a solid replacement for Google Drive.
If free storage is your thing, you can get even more with Mega. For something geared more towards business and collaboration try Box.
Mailbox.org offers email (at their domain or yours), plus a suit of associated tools such as a calendar and address book. All this for a very modest sum of money (and no data).
If you are willing to pay a little more FastMail offers a similar set of tools, but with a little more polish. For free and simple webmail check out ProtonMail.
As a user friendly, privacy conscious search engine, DuckDuckGo makes an excellent replacement for for Google Search.
You can actively do good while searching with Ecosia, who use their profits to plant trees. If you want the results from Google's algorithm, but not the privacy concerns, that's exactly what Startpage.com offers.