PSP Emulation
Manufacturer: Sony / Release Date: 2004
The massive Sony breaches of 2011 and 2012 weren't good for the company's customers, but they did provide one major benefit to the emulation community: the leak of the cryptography keys used to protect the PS3 and PSP at the most fundamental level, meaning the consoles could be completely jailbroken and made to run anything.
PS3 emulation on the PC still has some technical/architecture barriers to overcome, but PSP emulation is very advanced at this point. And if you have an actual PSP console, there is now a wide variety of emulators for other systems and homebrew software that can be easily run.
PSP Emulation Guide for PC
Recommended Emulator: PPSSPP (Windows, Linux, Android, iOS)
PPSSPP is about the most straightforward, easy to use emulator you'll encounter outside of the 8-bit and 16-bit consoles. It really is just unzip and go, no BIOS files needed, I didn't even need to configure my Xbox USB gamepad. Very good compatibility, runs well. Easy peasy. Another cool thing about it is that it's being developed for multiple platforms in tandem - Android, iOS, Linux - and you can move save and configuration files between the different versions.
Minimum System Requirements: Low-End Emulation
Running Emulators on a PSP System
The first step in running any "unapproved" software on a PSP is to install a custom firmware. This is a very simple process that won't permanently alter it. The one I've been using for nearly a decade now is CFW Pro-B (current version 6.60). I keep using this one because it's never not worked with anything I've thrown at it.
Just follow the install instructions, which simply involves hooking the PSP up to a computer by USB and copying some files over. Once Pro-B is in the right place, on the PSP go to your memory stick and you shold see a Pro-B icon. Fire it up and the PSP will reboot into the jailbroken version (it'll return to normal once you hard power off). The only difference you'll notice in this version is that any games / software you've added to the appropriate directories will now appear and be launchable from your memory stick.
There's a whole world of emulators you can run on the PSP, it's too much to get into here in detail. But as a general rule of thumb, the PSP handles up to the 64-bit generation well (PS1, which it has native emulation for, and N64). Basically once you get to the Dreamcast and beyond it's getting to be too much for the hardware. I haven't tried out anywhere near the whole field but I can tell you that the NES and Genesis emulation is excellent and the SNES emulation is generally pretty good. You can get leads on everything that's available at this page.
Peripherals:
* PSP 3000 (recommended version if you want an actual console)
* Pro Duo adapter (if you want to use a MicroSD card)