King Crimson - The band that pretty much started progressive rock and still the best - In The Court Of The Crimson King, Larks Tongues In Aspic and Red are essential listens.

Genesis - a band of two eras, both pretty good. The Peter Gabriel era has some of the best songs in the prog cannon with Selling England By The Pound, Foxtrot and The Lamb Lies Down On Broadway being essential listens. The Phil Collins era merged the catchiness of pop music with the complicated compositions of prog with essential listenings being A Trick Of The Tail, Wind And Wuthering, Abacab and the self titled. If you like live stuff than Genesis Live and Seconds Out are great listens.

Yes - Maybe the most beloved prog band due to writing catchy songs without compromising their progness - The Yes Album, Close To The Edge and Fragile are essential listens.

Gentle Giant - One of the strangest of the prog bands with unique vocal harmonies and compositions inspired by medieval music. Octopus and Free Hand are essential listens.

Emerson, Lake And Palmer - a band synonymous with arena prog, they were easily the biggest prog band during the genre's peak in the 70s. Essential listens are Brain Salad Surgery, Pictures At An Exhibition and the first album, which is self titled.

Rush is always a good choice. Subdivisions is a personal favorite.

I'm surprised no one has said Mars Volta. Most people love Deloused in the Comatorium but I'm partial to Bedlam in Goliath.

the only prog I know is like, dream theater? Is Opeth prog rock

I tried to stick to just prog rock, but there’s a bit of jazz fusion in there, too. I could do more for prog metal as well as for more funky stuff (Jacob Collier, Snarky Puppy, maybe some Moon Hooch).

Steven Wilson - The Raven That Refused To Sing

Steven Wilson - Routine

Storm Corrosion - Drag Ropes

Opeth - Coil

Impact Fuze - Moscow

Frank Zappa - Andy

Cloudkicker - Let Yourself Be Huge

The Paper Chase - We Know Where You Sleep

maybe some the decemberists?

I've recently been getting on to Haken and I've been really enjoying them. Their album the mountain in particular has been on repeat for me.

Edit: also give Goblin look they're an Italian group that's been around in a few incarnations since the 70s.

Porcupine tree, genesis, yes, rush, opeth, steven wilson, dream theater (start with panic attack), king crimson, pink floyd, tool, frank zappa, Hocus Pocus by focus, The Ocean, Loathe, the pineapple thief, a perfect circle, and my absolute favourites are

Storm corrosion, chroma key. Both of these are calming, haunting, ethereal masterpieces that can be listened on loop forever.

I'm definitely bleeding out of the genre at this point but they all at least have a prog vibe.

Also I don't know if this even counts as prog or what it even counts as but Cardiacs has some good songs.

https://nospun.bandcamp.com/album/opus

like early haken x late 90s dream theater, but also kinda different in afunky/souly way I can't quite put my ear on

I love Alan Parsons Project's I, Robot (1977) and Turn of a Friendly Card (1980) - another album that has not been mentioned is Rush's Moving Pictures (1981). Kansas' self-titled debut album (1974) is also pretty good, and it has John Brown on the cover.

Magma

itt: I found a YouTube link in your comment. Here are links to the same video on alternative frontends that protect your privacy:

I like Frost*, Haken, and Papadosio to name a few.

Hey OP, are you just looking for regular ole prog like tool, or broadly experimental, mathy, etc?

The Dear Hunter, they're my favorite band of all time. Theatrical/symphonic prog with an incredible vocalist.

Regress + The Moon / Awake

The Bitter Suite IV and V: The Congregation and the Sermon in the Silt

Ring 4 - Patrol

Mustard Gas

Los Jaivas, especially the album Aluras de Machu Picchu especially the songs Sube a nacer conmigo hermano and La poderosa muerte

They combine prog with andean instruments

Quicksilver Messenger Service if you like the more psychedelic side of the genre

Gonna second the calls for Haken. Pareidoilia or Veil would be great tracks to start with.

King Gizzard and the Lizard Wizard's PetroDragonic Apocalypse; or, Dawn of Eternal Night: An Annihilation of Planet Earth and the Beginning of Merciless Damnation was a great release this year as well.

I'll also recommend The Ocean, who have a fun naming convention for their albums. https://www.youtube.com/watch?v=BPMrwSwl8is

More metal than rock, but The Hirsch Effekt are fantastic. Their latest album is a 10/10 in my book.

My fave prog album: https://en.m.wikipedia.org/wiki/The_Death_Defying_Unicorn

Along with some other commenters are naming, I've been digging into Polyphia recently. Don't expect funky time signatures or even vocals, but the technique and timing is very math/prog.

1973's Metaphysical Animation, which only got any kind of an official release a few years ago. The only copy is from an acetate someone had hanging around, it's a cool album.

E: proggers

https://www.youtube.com/watch?v=lT-l4H-wIb4

Also I've listened to this 3 times in the past 72 hours

Protest the Hero are awesome. They've been making feminist music since day one.

https://www.youtube.com/watch?v=8Vo-bBA3-yY

the instrumental band covet is on the chill side. like a softer animals as leaders without the djent, and the guitarist does some novel technique when she plays that probably matters to people who are into that.

Plini is great, especially Selenium Forest.