There are multiple reasons to look for browser-based Game Engines:
Some of the Game Engines listed here are quite unique too, so you may find something interesting to use even if you weren't looking for something browser-based.
The main requisite for listing an Engine here is to be able to make and share a game entirely from browser. They also have to have a stable version launched, and community size will also be taken into consideration. Game Engines geared towards the classroom (Scratch, GameSalad) are not listed.
So, without further ado, let's check the list!
Construct 3 is one of the most popular proprietary engines for 2D games, on top with Game Maker. It has tons of official tutorials and assets, has its own browser games platform you can use to publish your games for free, a long list of features and it probably got one of the best guided tours to understand the basics of the Engine that you can play in your own browser. Constuct also offers a very intuitive Visual Scripting option for developers that prefer it over coding in Javascript.
It's still an Engine you have to pay a subscription for, and at $14.99/month it might be a little steep for most developers. But you don't need to go too far to know some of the really heavy-weight game examples made with Construct 3 such as Small Saga , Mighty Goose and Creature Keeper, so it's definetly worth it to check Construct 3 out.
Often described as the "free Construct 3 alternative", GDevelop stands on its own as a great open-source Game Engine with a similar visual scripting style. Similar to Construct 3, it also has plenty of official tutorials and community resources. GDevelop is open-source but it does have an optional subscription if you want to get more from its online services, such as the amount of times you can publish to Android/Desktop (once per day on the free tier).
Also similar to Construct, GDevelop has the website gd.games where you can publish your browser games.
PlayCanvas is not only a browser-available engine - it is browser first, so its Editor was optimized to be used in browsers and collaborativelly. The Engine also focus on general interactive 3D content development, and it has strong Web 3D rendering capabilites.
The Engine behind the editor is open-source, but the Editor is not, and the only way to use it is via their website. It is also subscription-based, but the main difference from the Free Tier to paid tiers is the ability to create private projects and more storage space for your projects.
MicroStudio is the much-simpler 2D cousin of PlayCanvas - a browser-first, collaborative-friendly Game Engine. It features it's own "simplified Lua-like" scripting language called microScript, but you can also code in JavaScript, Python or Lua.
MicroStudio also contains very handy in-engine guide and tutorials, and have an impressive set of (real-life!) languages that it supports both in its editor and in the documentation.
Twine is an Engine to create text-based interactive stories of the "gamebook" kind, so it does have many more limitations than other Game Engines - but for the task of creating interactive stories, there is hardly a better game engine (browser-based or otherwise) than Twine, thanks to its easy-to-use UI and domain-specific scripting language.
Bitsy is also an Engine to create interactive stories, but it creates them in a totally different way than Twine. While Twine is an Engine for text-based interactive stories like old-style gamebooks, Bitsy games are very unique in style, creating a "bitsy-like" genre on itch.io. If you want a very simple-to-use tool to create unique little narrative experiments, Bitsy might be the perfect tool for you.
TIC-80 is a Fantasy Console, a class of Game Engines covered in another post - suffice to say they are Game Engines that lightly emulate real-life limitations of old game consoles, and offer a full suite of tools to create your games on a single program (sound, sprites, tilemap, code). TIC-80 is an amazing Game Engine if you're planning to make a retro-like game.
Modd.io is an interesting Game Engine/Metaverse ecosystem of games that seems like it's trying to go in the direction of a "2D Roblox for browsers". It's still somewhat limited in the kinds of games it can make sing its visual scripting, but there are good examples of games to play in the website and a growing community on their Discord.
Also worth noting that Modd.io is a completely free and open-source Game Engine, so you can deploy the game engine locally if you want.
Puzzlescript is probably one of the most unique Game Engines of the bunch. It is a pure-code, browser-based Game Engine in which you code in, well, Puzzlescript - a script language to create puzzle games. The main difference between Puzzlescript and other progamming languages is that you'll describe the rules of your game declaratively, and the game comes to life from the rules you described.
It sure does limit the kinds of games you can make, but like Bitsy, it also has a big community creating games on itch.io. If you are interested in making a puzzle game, take a look at the games made with Puzzlescript first so you know how far you can go with this very simple tool.
WickEditor is in a tight spot on this list. Technically it is a browser-based "Macromedia Flash-like" Game Engine - it has a timeline, a similar set of vector drawing tools, you can script animations, etc. - with better native tools for publishing content in HTML5. That's an amazing idea and it would certainly be an unique tool among all of the browser-based tools of the list.
Unfortunately, as of 2024 WickEditor has been discontinued and it is no longer in development (last commit was from 2021). The reason WickEditor is still on the list is the fact that the tool is stable enough to be used for games, and its community is alive on the WickEditor forum. If you miss the Flash-era of games and wished to use something similar, WickEditor might be able to scratch that itch (and hopefully helping the community reviving the development of the Engine!).