The Anime Index, a HUGE list of streaming/downloading sites and apps categorized in Languages, Sub/Dubs and more.

Downloads

Nyaa (Torrent) - The Best Public Tracker to get Anime from.
        Sukebei (Torrent) - The Best Public Tracker to get Hentai from.

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.

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.

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.

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.

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.