With Bloodstained getting Classic Mode, I've been wondering what other games GOG has that are similar to the older Castlevania titles.

Basically, these are games with these characteristics:
* Game is a 2D sidescroller.
* Game is strictly linear, played one stage at a time without backtracking.
* You have a health meter. (In other words, health is handled in a typical manner, not like in Super Mario Bros., and not like Celeste either (where you die in one hit).)
* There aren't permanent upgrades. You might find a whip upgrade that lasts until you die, and you can get sub-weapons, but can only carry one sub-weapon at a time. (Well, Ninja Gaiden 2 and 3 did have a permanent subweapon ammo upgrade, but that's all it had.)
* Pick-ups are typically found by hitting candles (or something similar) with your weapon. One of the pick-ups (Hearts in Castlevania) is used as ammo for your sub-weapons.
* There are bottomless pits, as well as enemies that like to knock you into them. (If you've played any of these games, you know what I mean.)
* You have a limited number of lives, and if you lose them all, it's game over. (The game may allow you to continue, but for example continuing after a game over in 4-3 might send you back to 4-1.)
* In particular, for purposes of this topic I am not looking for metroidvanias.

So, I know that we have:
* Bloodstained's Classic Mode (but not the main game, which is a metroidvania)
* Castlevania 1 and 3 from that Castlevania/Contra collection

So, any other similar games on GOG?

(Shovel Knight doesn't quite qualify, as sub-weapons in that game are permanent upgrades, and you can switch between them in the menu. Note that this criterion would technically disqualify something like Castlevania Legends.)

Edit: Why the low rating?

Oniken should check off all those boxes:
https://www.gog.com/game/oniken

Slain: Back From Hell
https://www.gog.com/game/slain

You might wanna take a look at Volgarr the Viking. No health meter or sub-weapons though. Great game in any case.

Um, Oniken, Odallus the Dark Call, Realms of Chaos maybe?

Volgarr
First half of The Messnger, supposedly.
Odallus maybe?
Alien Rampage maybe

Jazz 1-2 are similar, besides having maze-like levels

The Messenger is supposed to be a homage to the classic Ninja Gaiden games. I wasn't a big fan of it personally, but I believe it meets most of your qualifications.

Odallus is excellent, classic-lite pixellated fun.you will not regret it. It feels like an early lost Castlevania sequel.

Slain is great as well, and has a Super Ghouls n Ghosts kind of feel. Good game with side-scrolling platforming and combat fun. It's also pretty difficult.

Funny thing is, some time ago I made a topic asking for metroidvanias, and Odallus was mentioned there, so I now have conflicting information about the game.

Also, I bought the game some time ago, but haven't gotten around to playing it. Maybe I should?

It's not too much of a metroidvania, if I remember correctly. You can get a few upgrades that boost damage or defense permanently (armor 1, 2, 3; sword 1,2,3). I think, there are also a few items which let you access new areas of a level (like scale of diving, armlet of pushing, or so), but level progression is still fairly linear. The game also consists of levels, not one connected game world.

I would overall call it more of an arcade game with some metroidvania elements, but ultimately it feels more like an arcade title, than a metroidvania.

Out of the more recent title, The Messenger might fit the bill, but I have neither played nor looked into it, beyond flicking through screenshots: https://www.gog.com/game/the_messenger

Disney's Hercules is also surprisingly close to that description, although I don't know if it has bottomless pits:
https://www.gog.com/game/disneys_hercules

I'd recommend either Lion King, Aladdin or Jungle Book over Hercules though. That game is rather sloppy and frustrating. But these are all a bit less straightforward than a JP action game, JB is basically a maze/collectathon platformer.

You stole my words :)
I also liked Odallus, but couldn't finish it. Oniken, yes, except the secret level, the might interest the OP as it has a female character (not the rest of the game).
Slain is gorgeous and has great boss battles but be warned it has a heavy metal soundtrack.
I consider Odallus a metroidvania. You have a bigger map that expands as you progress and you return to older levels with your new abilities.

In Butcher there's literally people falling from above causing you to fall into lava pools.
Blazing Chrome, very hard run and gun. Semi linear I think, like you can choose a level in a world, if I'm not mistaken, but can't roam freely. Same team as Oniken and Odallus.

So that knocks out Igavania type games then.

And then there's today's new release.