Wotaku, a HUGE list of Streaming/Downloading sites and apps categorized in Languages, Sub/Dubs and more.
The Anime Index, a list of Tools, Apps and Sites for your Anime needs.

Downloading

Nyaa (Torrent) - The Best Public Tracker to get Anime from.
Sukebei (Torrent) - The Best Public Tracker to get Hentai from.
Use Japanese titles to get beter results.

The Anime Index (DDL / Torrent) - This site also has Download sites/apps for Anime/Hentai/Manga and more.

AnimeTosho (Torrent) - Collates Releases from Public Trackers, and has DDL links for file attachments (Subtitles, Fonts, Chapters, Tags).

AniDex (Torrent) - Alternative Tracker to get Anime from, A Few Releasers post exclusively here.

AniRena (Torrent) - General Tracker for everything Japanese.

Tokyo Toshokan (Torrent) - A Library for every type of Japanese Media, shared with Torrents.

Nibl Bots | AniMK (XDCC) - Sites indexing IRC Bots where you can Download from using IRC Clients.
Check the AnimePiracy Wiki for a detailed guide into XDCC.

Release Indexes

A Certain Smoke's Index - A big list of the best Releases for Anime (by Seadex).

A Certain Fansubber's Index - Another list of the top Quality Releases for Anime.

Apps

qBittorrent | Deluge | Transmission - Free, Lightweight and open source Torrent Clients.
We do not recommend using µTorrent or BitTorrent, as it came bundled with Adware, Spyware, and Crypto-Miners in the past ^[1]. In its current state, it's Adware and Bloatware. We don't recommend using µTorrent v2.2.1 either due to confirmed Security Exploits.
        qBittorrent Enhanced Edition - A qBittorrent fork with enhanced privacy (IP filtering, auto-ban bots and copyright trolls, auto-update public trackers).
        qBittorrent Guide - A guide for configuring qBittorrent.

IDM | JD2 | XDM | Motrix | FDM - Download Managers that can boost Download speeds. Motrix and FDM support Torrenting, XDM is best for capturing downloads from your Browser, and JD2 is best for downloading multiple files simultaneously.
        Elephant - Adds YT-DLP support to FDM, meaning it can download from all these sites.
        JDownloader 2 Guide - A guide for setting up JDownloader 2.

YT-DLP - Can download from over 1500 sites including: Crunchyroll, Funimation, SoundCloud, Bandcamp, PornHub and more. Link to all supported sites.
Actively maintained fork of the popular YouTube Downloader youtube-dl with more functionality.
Stacher - A modern YouTube Downloader, also a front-end/GUI for youtube-dl.
TubeDigger - Advanced Media Downloader, have wider support for capturing and downloading media.
AnyStream - Netflix, Amazon Prime, Hulu, HBOmax and Disney+ Downloader, officially supports up to 1080p.
FlixiCam - Netflix & Amazon Prime Downloader.

Taiga (Windows) | Trackma (Linux) - Automatically detects the Anime Videos you watch on your PC and synchronizes your progress with AniList, Kitsu, MyAnimeList and more.
A must have for Weebs.

Misc

The AnimePiracy Wiki - Comprehensive information about everything Anime Piracy. A MUST READ if you are interested.

AnimeThemes | Themes.moe - A huge collection of Ending/Opening Themes for Anime.

SauceNAO | Anime Scene Search Engine - Reverse image search engines for Anime, SauceNAO is also helpful in identifying sauce.

Senpai.moe | Monthly - Calender for upcoming Official Anime Releases.

BECAUSE.MOE - Search engine to find streaming services that offer the Anime you search for.
Accurate up to May 27, 2020.

DDL: Direct Download, where you can download a file from a server usually done through your Browser.

 

Torrent: A decentralised Peer-to-Peer file sharing protocol that is very common when sharing Pirated Content, since the file isnt on a single server that can easily be taken down.

 

XDCC: A computer file sharing method which uses the Internet Relay Chat network as a host service. In essence, it's a Direct Download.