Hopefully this is not against TOS, if it is, please nuke like GAF. Do not link roms

reproduction of the function or action of a different computer, software system, etc.
"software emulation of complete systems"

Emulation was a very big portion of my gaming life in my teenage years, and it's still the best way to have a collection and relive your young days.

Best Emulation Resources

http://gwht.wikidot.com/ GAF Wii Wikidot

May be a bit old and outdated now, but the Wii is an emulation powerhouse. From Atari to N64, you can build your library on your SD card or USB

Up to date Systems
3ds.guide 3DS Homebrew Hacking Guide

New 3DS is, in my opinion, the best handheld console ever made for emulation until the switch opens like a cracker. Use the above page to get your 3DS up to speed.

https://henkaku.xyz/ PSVita Hacking Guide

Vita means life, if you have a 3.65 console. The native emulators are not so optimized, but offer a better experience than the old PSP

https://wiiu.guide/ WiiU hacking guide

WiiU is a very capable machine. Sadly, the homebrew community is not as active and the potential is untapped.

http://www.retroarch.com/ RetroArch pack

Previously you needed Nesticle + Zsnes + Snes9x + Neorage. Now everything is in this sexy pack. Can be complicated to understand but a bit of reading is all you need.

https://retropie.org.uk/ Raspberry PI

Some would say that the PI is the cheapest way to get you started on emulation. From tinkering your settings to downloading premade images, the PI changes the landscape. You no longer need to hack a console now. Emulates up to PSOne tho

NEW Snes Mini Hackhi2

The GOAT system gets the GOAT controller and with Hakchii2 you have, pretty much, the perfect emulation package (With 1 GB or storage space) I have not tested this. Credit to the original Poster in GAF (RIP) Robin64