Anime: Anime-Planet (https://www.anime-planet.com/)
Books: Goodreads (https://www.goodreads.com/)
Movies/TV-Shows: Trakt (https://trakt.tv/) - Good integration with plenty of media centers, streaming services and video players for automatic tracking.

Haha I know this is super old but thought I'd chip in, as I love these kinds of sites. I see them in mainly two groups: to log collection or consumption.

Collection:
Books: LibraryThing
Movies/TV/Anime/Music (Digital): Plex
Music (Physical): Discogs
Comics: CLZ Comics

Consumption:
Anime/Manga: Anilist, using the Otraku app
Books: Goodreads
Movies: Letterboxd
TV: Serializd
Comics (specifically Marvel): Complete Marvel Reading Order (https://cmro.travis-starnes.com/)
Music: RateYourMusic, which I only log when I sit down and actually listen to an album.

Also, I'm not sure what it would fall under, but I try to track my video game achievements cross-platform via either Exophase or MetaGamerScore.

I use Letterboxd constantly, probably just as frequently as I'm on here lol

These are the ones that I use:
Anime & manga (and other east asian animation) - MyAnimeList, AniList
Blu-ray/DVD collection - Blu-ray.com
Comics - LeagueofComicsGeeks
Japanese language guide for shows (idk what else to call it) - JPDB
Movies & Short films - Letterboxd, IMDB
Pokémon Cards - Pokéllector
TV Dramas (live-action asian shows) - MyDramaList
TV Shows - Serializd, IMDB