Non-spyware software as cited by spyware.neocities.org:

Web Browsers

[link] BadWolf (minimalist but usable)
[link] Gnu IceCat
[link] Lynx (text-only)
[link] Iridium (after some steps)
[link] Falkon (DYOR, could have spyware on windows, not on linux)
[link] Netsurf (after some steps, extremely lightweight, uses own engine so mostly unsupported, no JS as of 3.11)
[link] Otter Browser (no spyware, but it uses old libraries, most likely with known exploitable vulnerabilities)
[link] Pale Moon (after some steps)
[link] Qutebrowser (keyboard-focused mostly like vim, minimal GUI)
[link] SeaMonkey (after some steps, basic)
[link] Surf (very basic)
[link] Tor (after some steps, might still have some spyware, changing settings may increase fingerprinting)
[link] Ungoogled-Chromium (one of the best Chrome-based spyware-free browser)
[link] Web Browser (based on Pale Moon)

Messaging Clients/Services

[link] Hexchat (standard IRC channels aren’t encrypted, might leak IP addresses, local conversations, pretty much only good for privacy, not anonymity, FOSS)
[link] Signal (not listed, but safer than Hexchat, at rest cryptography on Android is not supported anymore)
[link] Molly (not listed, Signal fork for Android with rest cryptography added back in, plus other positive tweaks)
[link] Session (not listed, anonymity-focused Signal fork, requires no phone number, out-of-the-box onion routing, apparently not secure, though there’s also this response, so DYOR)
[link] qTox (not listed, public key identification, full anonymity, P2P, IP might be exposed if no VPN, FOSS)
[link] Matrix (not listed, decentralized, can be self hosted, server can know who is talking to whom and message lengths, some unencrypted metadata, user’s IP address is exposed to server, FOSS)
(btw Discord, kinda funny)
(btw Telegram is not perfect)

Search Engines

[link] DuckDuckGo (marked as possibly spyware, but it’s the only non-extremely high listed)
[link] Startpage (not listed, but afaik superior than DuckDuckGo in privacy, while still getting results from Google. DYOR)

Music Players

[link] VLC (duh)
[link] Musicolet (not listed, allegedly no internet connection, downloadable from high-risk sources for privacy, possibly biased so DYOR (i use it))
[link] Strawberry Music Player (not listed, FOSS, GPL license, Clementine fork, DYOR)

I will keep updating this with more categories and software as I do more research until further notice. It is currently incomplete, though informational.
I shall warn you, take this list with a grain of salt. It may be outdated in several ways, as I do not actively monitor all of these, and there may also be nuances you should know before any decisions affected by this list. I strongly recommend you to DYOR, as this is merely an entry-level project.

It originated as a quick Discord message, so the format may also change slightly as I see fit.

woof :3