It might help if you define what an RPG is to you.

Every game classified as an RPG that I know of has a growth system, usually in the form of XP (the TES games from Daggerfall onward being the exceptions that come readily to mind). For some, this is one of the defining mechanics of an RPG, if your character doesn't get stronger, it's not an RPG (I don't necessarily agree with this viewpoint BTW).

From the way I see things, the closest you might get is a game (FPS most likely) with RPG elements, usually in the form of an ability unlock, but these are clearly not RPGs.

I think,there is plenty that can be modded that way.And like IwubCheeze says it depends on YOUR definition of RPG's as we all have different ideas.

Isn't that called Adventure game? Zelda fits everything in rpg description except it's item based progression instead of statistic based, and it is defined as Action Adventure

Isn't that mutually exclusive? I mean if a game doesn't have any sort of progression system then it's debatable if it's an RPG.

Closest thing I can think of was Heroes of the Lance for the NES.The characters had D&D stats but couldn't level up or get stronger IIRC.

Maybe Gauntlet - your characters are hacking their way through a dungeon but can't get stronger.

Isn't RPG without level progression or equipment upgrades is basically just adventure games? So probably Sierra games (if you want older classics) or Telltale games (for newer sensibilities).

Or you can just play any number of RPGs and challenge yourself to finish the game with the starting gear and without leveling up.

If you can't improve your character in any way, not even by getting better equipment, it's not an rpg imo.
There are of course rpgs like Age of decadence where the core physical attributes like strength, dexterity etc. are fixed and can't be raised during the game (except by special means), but even there you have skill progression and get better equipment.
I have to say, I seriously wonder how one can come up with such bizarre, nonsensical questions as you regularly do. Must either be some form of autism or trolling,

Well, there is Undertale. Yes there is a progression system but one of the paths through the game requires you to never get stronger.

A growth system generally allows you to feel stronger over time, getting better, simulates your character... getting stronger, faster, more skilled, or luck just going to your favor more often, etc etc...

So an RPG without a growth system. These are going to be few and far between probably, but not impossible to find. But assuming you go purely on equipment that can get better, that too is a growth system. Diablo series for example is far more equipment strength vs skills/personal growth.

Questron and Ultima have growth of the 4 stats but otherwise has no growth system, and those you can only get via playing mini-games, so if you avoid the mini games you don't have a growth system. (well, beyond getting better equipment). Ahh i remember exploring for hours, fighting monsters and getting chased by guards once i beat the casino games... Reminds me of Wolfenstein too... weak on the RPG aspect but a good adventure...

I saw a project for Final Fantasy X where there's a challenge you can play through pretty much the ENTIRE GAME without ever putting a point on the sphere grid. (The final boss being the only thing that they couldn't quite complete on that range)

If you go earlier/older games, i was looking for a few, I think Dragon Quest for Atari has a roll system for creating a character but i had seen no way to improve the character. (or maybe i couldn't leave the dungeon to spend the XP, not sure. Cheating i find the stats do almost nothing for you anyways)

Text adventures might be a good place to check out. They are RPG's in a sense, and rely more on knowledge you accumulate and far less on skills.

Another World might qualify...

Reminds me of the NES gargoyle game, the only 'growth system' was how long you could flap your wings (once, twice, three times, or infinite) and was more to unlock areas and less about growth...

MagicMaker is Sorta an RPG, the only 'growth system' i remember is getting better gems/magic to put in slots...

Defender's quest, if you drop the difficulty to minimum you can play through with nearly no leveling...

And if you consider speedruns, i've seen speedruns of both Morrowind and Fallout where no leveling was done and they beat the game within 15 minutes, so depends on those approaches i suppose...

Sorcery! doesn't have leveling. It has a handful of better swords here and there but doesn't expect them.

I think this part is impossible, as the very definition of CRPG is debatable; people have rather different definitions for this.

As to your second point about not getting stronger, do you accept games where you can and are supposed to get stronger but can choose not to do so? Many games give you points to spend on getting stronger, but you can choose not to spend them. Does that count, or do you want games where it's designed for you to not get stronger?

I think games like that will either be shorter, so your non-advancement isn't an issue, or they'll fall into what might be called other genres. Some have mentioned adventure games... I'd mention PNC (point n click). They can tell stories but don't necessarily have levels/growth.

VTMB gives you xp to spend on sklils and stats, but you dont' have to spend them. But regardless, you can never increase your hit points or blood pool... those remain constant throughout the game. Deus Ex gives you skill points and augmentations to improve your character, but you don't have to use them.

Warlock of Firetop Mountain may not have growth... I've looked at the trailer but don't see any indication of it.
http://store.steampowered.com/app/324740/The_Warlock_of_Firetop_Mountain/

Though it's not a video game, but rather a series of which-way books that have been converted to an interactive reader, you may enjoy The Lone Wolf series by Joe Dever:
https://www.projectaon.org/en/Main/Books

While there is some growth, it's mainly between books, not during. The books are for young adult and I enjoyed them as a kid... I still recommend them today.

Define a growth system, please.

I think I understand what you are going for but I really cant think of any. Most Role Playing Games have some form of progression, be it the PC leveling up or simply obtaining more and more powerful loot. If you want a game where the PC gains no strength but your weapons improve I could reccomend the Monster Hunter franchise but, aside from that I really wouldnt know where to start.

Mages of Mystralia

RPG = Role Playing Game, so games where you are put into the shoes of someone (spoiler alert: a LOT of games do this), like Wing Commander for instance.

Progression systems actually have nothing to do with Role Playing itself, it's more of a sidegame for the statgeeks.