Recommend me a shoot 'em up game

any of the borderlands games but 3

Nuclear Throne is pretty cool. It's been on sale.

A good roguelike shmup is Binding of Issac Rebirth.

A horizontal shmup I remember very fondly is jets N Guns GOLD

Beat Hazard 2 and LUFTRAUSERS are pretty good.

The Alltynex Trilogy bundle is a good deal. Relatively low price for three great games. https://store.steampowered.com/sub/39160/

There's Monolith if you care about roguelites. It's most likely the closest one in the genre to a traditional shmup and easily one of the best roguelites out there, too. Excellent game.

Astebreed is pretty good if you want a particularly flashy game.

For less conventional stuff you can look into Savant: Ascent, Switch 'n' Shoot (if you want a shmup you can play with one button) and Revolver Re:actor.

And Ikaruga, of course. But you probably already know this one.

https://www.gog.com/game/tyrian_2000

Good and free!

What have you played?

Countless shmups were made in the 80s and 90s. Start with anything by Toaplan. Yes, that includes Zero Wing, which is actually well-made, translation aside.

If you really want to stick with Steam/Gog then you might want to start with Raptor: Call of the Shadows.

Geometry Wars is always a fun time.
It's the perfect game for short play sessions, if you just want to make some carnage for a bit.

Um, can you give a bit more specification on what kind of Shoot 'Em Up games you're looking for? ;P

I presume the ones that fall under Bullet Hell would be ok, right? ^_^'

Jamestown (or its updated re-release) is a pretty good choice.

A lot of the games by Orange_Juice are really good bullet hell games. I can personally recommend SUGURI (thought it might be a bit... "old" and unpolished; also one of the achievements isn't working) and Sora (kinda a sequel to SUGURI which is why I'd recommend playing that one first; immensely improves on just about everything). They play quite a bit differently from most Bullet Hell games with their unique Dash mechanic (which makes Sora on the "very easy" side as far as Bullet Hell goes).

I'd also recommend the Gundemonium Collection (Gundemonium Recollection, GundeadliGne and Hitogata Happa - I should warn that this last one is particularly hard) but unfortunately due to publisher issues they can't be bought directly in the Steam Store right now and I have no idea if keys are still available anywhere. T.T

If you're also including "Twin Stick Shooters" under Shoot 'Em Ups then I have a few more I'd recommend. :D

Crimsonland is an old classic which still holds up today. :)

RIVE is a hidden gem which almost no-one knows about (but they really should).

And Intrusion 2 is another hidden gem which I hope slightly more people know about with a very interesting psychics engine.

Edit:
Here's some more:
Bit Blaster XL is nice and short (and cheap). ^_^

All the Chicken Invaders games. :D

All the Metal Slug games. (Personally I've only played METAL SLUG 3 but they're all conceptually similar.)

https://store.steampowered.com/curator/39372135-Lists-of-Niche/list/79130

Here's a slice of what I have in my "Shmup" category in my Steam Library (and a few that I haven't gotten around to picking up yet, but look pretty good). I'm sure something in here will appeal to you:

Crimzon Clover WORLD IGNITION
R-Type Final 2
Ikaruga
DELTAZEAL
XIIZEAL
Jets 'n' Guns Gold
Redux: Dark Matters
Sine Mora EX
Ether Vapor Remaster
Syder Arcade
Vortex Attack
Xenoraptor
Satazius
Rigid Force Alpha
DARIUSBURST Chronicles Saviours
Devil Engine
ZeroRanger

ZeroRanger and Blue Revolver are some nice vertical shoot em ups.
Touhou Luna Nights is a 2D action game with great shoot em up styled boss fights if you'd care for something outside of the classic style; see Assault Android Cactus+ for a Twin-Stick Shooter with similar elements.
And currently on sale are Danmaku Unlimited 2 & 3, Q-YO Blaster, Vortex Attack and R-Type Dimensions EX.
Many more as well, some listed by other commenters.

https://store.steampowered.com/app/39800/Nation_Red/

Bullet Party is decently priced and has 180 levels that are packed with action and are usually completed under a minute.

Blazing Beaks, nice in coop. Prepare to die quite a lot ;-)

My favourites are:

Syder Arcade
SkyForce Reloaded / SkyForce Anniversary

• Steredenn (And a nice rediscovery when cleaning my backlog : Retro-style bullet-hell, very addictive. )

• Aqua Kitty - Milk Mine Defender : An Arcade classic, but with fishes and kitties.
  (...And Astro Aqua Kitty, if you don't mind another kind of playstyle, more "Spelunky-like"... Also, this game still have no cards yet.)

CAVE unfortunately stopped with the Steam releases, but Mushihimesama is a must have classic for a shmup fan. They also have Deathsmiles and DoDonPachi Resurrection
I personally really liked ALLTYNEX Trilogy, only RefleX has no achievements.
Neko Navy is not a particularly well known game, but it's worth a shot too.
And for a freebie, there's Jigoku Kisetsukan: Sense of the Seasons.

Epido on steam is a good simple game for cheap, its got achievements, cards, etc. It is a lewd game though so idk if that's your thing lol

Jets n Guns Gold is really good, and have a killer soundtrack

ZeroRanger is a very interesting take on the genre

AKxolotl hasn't come out yet, but it looks promising

Steredenn and Luftrausers were both very good shmups that I struggled, but managed, to complete 100%

I wouldn't count Binding of Isaac as a shmup but it's an addicting twin stick shooter with an insane amount of content for a 1GB game. I've spent 250 hours to get 250 of the 637 achievements available with the full game (Rebirth, Afterbirth DLC, Afterbirth+ DLC, and Repentance DLC)

you absolutely HAVE to play ULTRAKILL if you like shooters. It's the best rated game of all time on Steam (percentage based). It's amazing.