Photo: Evan-Amos, Wikimedia Foundation.
The jailbroken Nintendo 3DS is the 2nd-most powerful emulation machine that you could ever hope to put in your pocket. Apart from the literal thousands of games released for the 3DS and DS lines, you are also able to unlock the entire back catalogue of games from most of the consoles released during the 1977-2001 period of time. Though infeasible to emulate the 3D home consoles of the time, the 2D ones are absolutely in the pocket, and it's only as hard as installing a program from Universal Updater. You do, however, require a jailbroken console, since none of this will be able to run on a stock-condition system. Fortunately, 3DS.hacks.guide has all the information you'll need to make that happen, at extremely little risk to you. As long as you follow all the instructions in the order they're given, you'll reduce the risk of bricking even your release-day model 3DS to as near to 0% as you can get in a universe that has no absolutes. It's easy, it's fun, and it's free; all you need is a blank SD card and a dream in your heart.
So, what can I play, then?
Nintendo.
Nintendo 3DS
Nintendo DS
DSiWare
Game Boy Advance
Nintendo 64 (if using a New Nintendo 3/2DS)
Game Boy Color
Virtual Boy
Game Boy
Super NES
NES
Sega.
SG-1000
Master System
Mega Drive/Genesis
Game Gear
32X
Mega-CD
Atari.
2600
400/800/5200
7800
Lynx
Others.
Mattel Intellivision
Colecovision
Sinclair ZX Spectrum
MS-DOS
MSX
Doom (via PrBoom)
Dunhuang Super A'Can
Essentially, this represents the entire battery of 8- and 16-bit game consoles, some 8-bit home micros, and MS-DOS. While this is adequate to scratch most retrogaming itches, the Wii U is actually the absolute top-end jailbroken emulation machine, being able to play games for itself, Wii, and GameCube natively before any emulation needs to happen. If you're trying to replace your smartphone as a gaming device, the 3DS makes more sense, as it is far more portable than the TV-only Wii U. Why not just jailbreak the Switch? Mostly because jailbreaking this system requires opening the hardware casing and soldering on a new chip. It's best to wait for now and see if software-based exploits can be found that are unrelated to the (now quite old and fully patched-out) fusee-gelee exploit, since making physical modifications to a printed circuit board requires intense training, fairly expensive tools, and a good deal of experience. But, if you have a Switch and you know a girl with a soldering iron who makes her own voltage-control oscillators from scratch, go ahead and commission her to put a modchip in.