My favorite PSX emulator ! It runs on macOS, Windows, Linux and Android. The Android version often lacks the latest and greatest features especially on the PlayStore, consider GitHub sources on Android.
A great PS2 emulator with an 
Android version alongside computer ones.
This one does NOT require you to load a BIOS file.
THE PS3 emulator, there is no concurrence, it runs on Windows, Linux and now also Mac (still experimental). It has improve a lot and is really impressive now with a lot of games labeled as "in-game" that will run from start to finish with a pleasant experience!
An Android-specific fork of RPCS3. Start to be interesting but not really playable in most titles.
We're getting here ! It's still in early stage, don't expect much of theses for now
THE PSP emulator ! Works on macOS, Windows, Linux, Android, iOS and more The PPSSPP Gold is for supporting the devs so buy it if you like it !
The first PS Vita emulator and the only one that can run commercial games that I'm aware of. Still experimental !
A modded version of the controversial 
GameHub (PC games on Android) that removes unnecessary permissions, limit telemetry and proxies your connection through their servers (you can selfhost the server yourself)
If 
GameNative didn't work for your games try this one.
To emulate Windows (or Linux) on Apple devices
Worth mentioning if you need better performance: 
Parallels Desktop mac only
A great OG Xbox emulator for macOS, Windows and Linux with now support for Vulkan, which has not bring impressive optimization yet but that we could see improving in the future.
Worth mentioning: 
Cxbx-Reloaded Windows only
THE 360 emulator ! Only on Windows, but can run on Linux through Wine/Proton !
There is a front-end named 
Xenia Manager that makes the installation, configuration and usage easier. It is still early and a bit buggy using but a promising project to make the emulation easier for non tech savy people. And it did improved since the first time I tried it.
Other options are 
X360 Manager and 
Xenia Dashboard
These are translation-layer similar to Wine/Proton for Windows 10/11.
Currently only https://alternativeto.net/software/windurango/about/ is publicly available and only works with Minecraft.
The best way to emulate Xbox One and older is using an official Xbox Series.
The GX version works great for macOS, Windows, Linux, Android and iOS
Worth mentioning : 
Kega Fusion
The Sega Saturn emulator
Worth mentioning:
Saturn.emu Android Paid
Kronos Windows & Linux
Ymir is a very promising Sega Saturn emulator that might just become the standard in the comming years.
One of the greatest Dreamcast emulator, and it is free and open source.
For online features and games use this fork: 
Flycast Dojo
Google Play Games is now available on Windows PC, if you just want to play games this might be the easist and safest option even though you have to register with your Google account.
A nice Android emulator working on both macOS and Windows but like most option is bloated and not privacy friendly. I finded to be the best (especially after debloating it) regardless, 
BlueStacks is another great option.
Debloating guide : https://gist.github.com/TameemS/72c4b92131977aced56e727d51599a48 RECOMMANDED
Worth mentioning :
BlueStacks macOS/Windows
LDPlayer Windows - debloating guide : https://gist.github.com/TameemS/894cdb8adae1d6042a5f21c4e80bcd9e/
GameLoop Windows
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