Nintendo 3DS/Homebrew

Like the DS, the 3DS has a pretty active homebrew community. Even still after the release of the Switch. There's a compelling argument to make that with homebrew, the New 3DS is the ultimate portable game platform.
Make sure to check the DS Homebrew article for more.
To hack your 3DS, the guide at https://3ds.guide is the most accurate and best online. More homebrew can be found here.
A note: some of the more intensive stuff performs worse on the Old 3DS and 2DS. The New 3DS and New 2DS performs better with pretty much everything.
==Games==
Title 	Genre 	Description
Half Life (Xash3DS) 	FPS 	Yes, Half Life on the freakin' 3DS! Some crazy Russians managed to reverse engineer GoldSource and made it open source (Xash 3D). This port is based on that. Runs a bid sluggish on O3DS, but performs better on the N3DS.
Quake 1 	FPS 	Pretty great port. Even includes online multiplayer!
Quake 2 	FPS 	Pretty basic port. Runs in software mode, but performs decently.
Quake 3 Arena 	FPS 	Pretty good port. Somewhat sluggish on O3DS.
Doom (PrBoom) 	FPS 	Includes Music playback that the DS port lacks.
Wolfenstein 3D 	FPS 	Pretty basic port.
Duke Nukem 3D (EDuke3D)]	FPS 	Hail to the King baby! Runs pretty well. Sadly, Ion Fury isn't compatible but could be if someone bothers to update the port.
Lemmings 	Puzzle	It's Lemmings on the 3DS. Yep.
==Emulators==
Title 	System(s) 	Description
Retroarch	2nd-4th Gen systems, PS1, et.al 	Offical port by the libretro team. The basic cores (2048, NES) run full speed on O3DS, while everything else is near full speed. N3DS has better performance. Even PS1 emulation works extremely well on there (2d games, early 3d stuff). O3DS users might want to check on the other emulators below for better performance. N3DS users might want to stick with this for all your emulation needs.
mGBA 	Game Boy family (GB/GBC/GBA) 	Official port, developed along side the other versions. Runs pretty well. Also great for GB/GBC games as well. Supports the gyroscope for games that use it (WarioWare Twisted, Kirby Tilt N Tumble).
SNES9x 	Super Nintendo 	Most games run full speed on O3DS. SA-1 and Super FX chip games have performance issues. But on the N3DS, everything runs full speed. There's also BlargSNES if you're having issues with SNES9x.
VirtuaNES	NES / Famicom 	Good emulator, but not super accurate. Retroarch has Nestopia UE core if accuracy matters to you.
PicoDrive	Mega Drive / Mega CD / Master System / Game Gear	Pretty good Sega 8/16-bit emulator. Now has 32x and CD support, and is the fastest running option.
Old 3DS has some minor sound issues due to lack of 44kHz support in the emulator (you have to be a turbo nerd to notice), but New 3DS runs Genesis/MD mostly fullspeed and 44kHz is fully supported, so games sound normal.
==Utilities==
Title 	Type 	Description
TWiLightMenu++	Menu Replacement	An open source replacement for the DSi Menu. Can be used to launch DS and DSi games from your SD card slot. No Flashcart required. Also includes some neat features like cpu speed up for DS games.
If you get a white screen when booting the menu, close your 3ds for a few seconds, then open it again and touch the screen. Repeat process until you see the health warning menu.