I collected over 33 lists of Best Music of 2021 from the Internet, newspapers and magazines and compiled them into one meta-list. Here are the results: every recording on four or more of the original source lists, organized by rank (that is, with the albums on the most lists at the top).
Note 1: I have provided genre descriptions of the artist from Wikipedia as a guide.
Note 2: These are not my personal opinions. I have not listened to all this music.
Note 3: An asterisk means I own the recording.
On 33 lists
Floating Points, Pharoah Sanders, and the London Symphony Orchestra – Promises (jazz/ambient/dance)
On 21 lists
Tyler, the Creator – Call Me if You Get Lost (hip hop)
On 19 lists
Dry Cleaning – New Long Leg (art rock/post-punk)
Low – Hey What (indie rock/slow core/dream pop)
Little Simz – Sometimes I Might Be Introvert (hip hop)
On 18 lists
Arlo Parks – Collapsed in Sunbeams (R&B/soul)*
On 17 lists
Olivia Rodrigo – Sour (pop/pop rock/indie pop)
On 16 lists
The Weather Station – Ignorance (folk/experimental)*
Japanese Breakfast – Jubilee (indie rock/low fi/experimental pop)*
Turnstile – Glow On (hardcore punk)
On 13 lists
Adele – 30 (pop/soul)
On 12 lists
Mdou Moctar – Afrique Victime (rock/blues/assouf)
Snail Mail – Valentine (indie rock)
On 11 lists
Billie Eilish – Happier Than Ever (pop/electropop/indie pop)
The War on Drugs – I Don’t Live Here Anymore (indie rock/neo-psychedelia/Americana)*
On 10 lists
Wolf Alice – Blue Weekend (alternative rock/shoegaze/dream pop)*
Lil Nas Ex – Montero (hip hop/country rap)
Halsey – If I Can’t Have Love, I Want Power (synthpop/alternative pop/R&B)
On 9 lists
PinkPantheress – To Hell With It (bedroom pop/drum and bass/jungle)
Self Esteem – Prioritise Pleasure (experimental pop/indie pop)
On 8 lists
Arooj Aftab – Vulture Prince (jazz/minimalist/Neo-Sufi)
Squid – Bright Green Field (post-punk/experimental rock/ambient)
Nick Cave & Warren Ellis – Carnage (rock/alternative/indie rock)*
Lana Del Rey – Chemtrails Over the Country Club (baroque pop/dream pop/rock)
Doja Cat – Planet Her (hip hop/pop/R&B)
Black Country, New Road – For the First Time (experimental rock/post-rock/post-punk)
On 7 lists
Sons of Kemet – Black to the Future (jazz/Afro-beat/world)
St. Vincent – Daddy’s Home (rock/pop/art rock)
L’Rain – Fatigue (experimental)
Mach-Hommy – Pray for Haiti (hip hop/rap)
Cassandra Jenkins – An Overview on Phenomenal Nature (ambient pop/folk pop)
On 6 lists
Summer Walker – Still Over It (R&B)
Kanye West – Donda (hip hop/gospel/progressive rap)
Silk Sonic – An Evening With Silk Sonic (R&B/soul/funk)*
Dawn Richard – Second Line (R&B/pop/electronic)
Madlib/Four Tet – Sound Ancestors (boom bap/instrumental hip hop)
black midi – Cavalcade (math rock/noise rock/post-punk)
Yola – Stand for Myself (country soul/R&B/Americana)*
The Spirit of the Beehive – Entertainment, Death (alternative rock/dream pop/experimental rock)
Armand Hammer & The Alchemist – Haram (hip hop)
On 5 lists
Idles – Crawler (hardcore punk/indie rock/post-hardcore)
Illuminati Hotties – Let Me Do One More (punk rock/indie rock)*
Hiatus Kaiyote – Mood Valiant (neo soul/jazz-funk/future soul)*
Iron Maiden – Senjutsu (heavy metal/progressive metal)
Playboi Carti – Whole Lotta Red (hip hop/trap/cloud rap)
Lucy Dacus – Home Video (indie rock/indie folk)*
Tirzah – Colourgrade (trip hop/noise/R&B)
Yasmin Williams – Urban Driftwood (folk)
Vince Staples – Vince Staples (hip hop)
Grouper – Shade (psychedelic folk/dream pop/sadcore)
Jazmine Sullivan – Heaux Tales (R&B/pop/hip hop)
On 4 lists
Dave – We’re All Alone in This Together (hip hop/conscious hip hop)
James Brandon Lewis & Red Lily Quintet – Jesup Wagon (jazz)
Amyl and the Sniffers – Comfort to Me (pub rock/punk rock/garage rock)
Sleaford Mods – Spare Ribs (electro-punk/rap-punk/post-punk)*
Gojira – Fortitude (technical death metal/groove metal/post-metal)
Moor Mother – Black Encyclopedia of the Air (experimental)
Sault – Nine (neo-soul/R&B/funk)
Loraine James – Reflection (electronica)
Kacey Musgraves – Star-Crossed (pop/country-pop)
Anna B Savage – A Common Turn (art pop/indie folk)
Allison Russell – Outside Child (folk/country/Americana)
Julien Baker – Little Oblivions (alternative rock/indie folk/slowcore)*
Mustafa – When Smoke Rises (indie folk/R&B)
serpentwithfeet – Deacon (baroque pop/electronic/experimental)
Lana Del Rey – Blue Banisters (folk/pop/jazz)
Classical
Toumani Diabaté & London Symphony Orchestra – Kôrôlén*
Leipzig Gewandhaus Orchestra/Andris Nelsons – Sofia Gubaidulina: Orchestral works
Spektral Quartet – Anna Thorvaldsdottir: Enigma