Google Operating systems alternatives

Ubuntu Touch

Ubuntu, but for phones.

LineageOS

Open-source and based on Android, but without the crap.

SailfishOS

Privacy-focused mobile OS by Jolla with a proprietary UI and Android compatibility layer on top of an open-source Mer GNU/Linux base.

/e/OS (Murena)

A deGoogled Android fork from the France-based e Foundation, shipping with its own app store and cloud services instead of Google's. Aimed at non-technical users; also sold preinstalled on Murena-branded phones.

CopperheadOS

Secure Android built for encrypted and secure phones by a privacy focused company. Paid, commercial product sold to businesses rather than a free download.

GrapheneOS

Open-source Android-based OS with an emphasis on security and privacy. Features advanced hardening and privacy protections throughout the system.

postmarketOS

Open-source mobile Linux OS. Can install different user interfaces such as Plasma Mobile. Thanks @okias

Replicant

Free Android distribution. Puts the emphasis on "freedom and privacy/security".

CalyxOS

Open-source Android-based OS with an emphasis on security and privacy. Provides good combination of privacy and security together with usability. Optional support for MicroG.

DivestOS

DivestOS is an alternative Android ROM with enhanced privacy and security along with support for many older devices. It is an unofficial soft fork of LineageOS. Website also available through Tor.

GalliumOS

"A fast and lightweight Linux distro for ChromeOS devices". Based on Xubuntu.

Qubes OS

"A reasonably secure operating system", at least according to their website. Edward Snowden recommends it.

Subgraph OS

A desktop computing and communications platform that is designed to be resistant to network-borne exploit and malware attacks.

Tails

For the uber-paranoid. Runs live and the entire OS is routed through Tor right from boot. Built on Debian.

Knoppix

Another Live OS, runs from CD/DVD/USB. Can also be installed if desired.

Parrot OS

Debian-based and privacy focused. Fully sandboxed. (thanks u/Safe_Airport)

PureOS

The OS of Purism Laptops (mentioned in the Hardware section). Very clean UI. Editor note: I could not get this working on a UEFI Dell laptop. The group behind PureOS does not provide any UEFI support.

GhostBSD

This is a secure open-source OS based on FreeBSD, preconfigured to be a sane desktop environment for all users.

Any other form of Linux

Ubuntu; Debian; Mint; Fedora; Arch or Manjaro (Manjaro is objectively much easier to get running than Arch); Trisquel; Gentoo; Alpine (thanks u/privacyfreak555); etc etc etc

AsteroidOS

The cleanest (and only) open-source alternative for Wear OS. Make sure you buy a watch that supports it!

Kodi

It's incredibly powerful and backed by one of the strongest communities around. Tons of plugins to do nearly anything you want. Software installs on nearly any platform.

OSMC

Free, open-source media center OS. Kodi is pre-installed. Thanks to @g4rret and @lgiard for clarifying the difference between Kodi and OSMC!