Emulation: cause it's awesome!

Well, it's not the most noble act but in some cases it' can be pretty expensive to get your hands on the real thing...

In most cases it can be said: the older the system, the better the emulation. Plattforms like gameboy(advance),snes,nes, megadrive, master system, playstation 1, Nintendo 64 and some others are nearly perfect when it comes to emulation.

Dreamcast emulation is also pretty advanced. Some games may have minor graphic glitches but most games are very much playable. I can highly recommend Resident Evil Code Veronica and Shenmue here.

Another Sega platform, the Saturn works good in general but seems to have small conflicts with some graphic drivers, especially Nividia ones. For me that resulted in having a black border around my game screen.

For newer Nintendo plattforms: Dolphin: wich is a Wii and Gamecube emulator keeps getting better and better. Many games can be played without any problems on it. and if you buy an adapter to use a gamecube pad or wiimote on your pc it comes pretty near to the original experience.
DS also runs fine and in most cases the stylus can be well replaced by your computer mouse.

PS2 emulation works good in most cases as well but has higher system requirements than everything else posted above. At least if you want to get good fps.

From what I heard Xbox emulation basically doesn't exist except for one emulator wich is able to emulate Halo 1. And only that.

I have played tons of games via pcsx2. You can also emulate Nintendo Wii via Dolphin and play, for example, Xenoblade Chronicles. ;)

Sega Genesis\Megadrive and PSP emulators are a must try, unless you agree to try them and their best games, I'm not going to name all the best games till then, I've done it before and no one cared, wasting my time.

Dolphin - for Wii and GameCube
PPSSPP - PSP (of course)
Kega Fusion (still the best for Mega Drive/Sega CD/32X
DeSmuME - Nintendo DS
Mame or Final Burn Alpha - arcades like King of Fighters and Street Fighter

Wii U: http://cemu.info/

For SNES emulation I recommend Higan: https://byuu.org/emulation/higan/

Edit: And for Amiga game emulation FS-UAE with the database: https://fs-uae.net/ & https://oagd.net/

FCEUX for NES/Famicom
Stella for Atari 2600

Gaycube(Dolphin) and the Peest2(PCSX2) games gain the most from a resolution boost.

love emulation of old consoles, if you want the full 90s feel i recomend you trying something like Gameroom VR, is really cool to play NES or SNES games.

this are my fav kind of emulators, not only emulate the games but also the looks :P
someone did it to a miniNES xD

MAME is one of my favorites, having the classic arcade games(and even some of the more recent ones) right there on your computer and playing exactly the way they played at the arcade is just an amazing feeling... you can even buy kits on Ebay to build your own arcade control panels from real arcade parts to make it feel even more authentic... just add plywood. http://www.ebay.com/itm/2-Player-USB-Mame-Arcade-Kit-w-2-Joysticks-4-8-way-16-HAPP-Push-Buttons-60-in-1-/221973824045?hash=item33aeabc22d:g:eZUAAOSw~OdVWpbB
I've actually bought kits from this seller, and for the money, you can't really go wrong..... not at all trying to advertise for them, but if building your own control panel is something you might find yourself interested in, this is a good starting point!

I have used a variety of emulators, but the thing I noticed that regardless of which one you use; it will NEVER be as great as playing it on the original hardware. I always preferred playing it with the most accuracy, which even though the hardware of old was not as great, to emulate such hardware and the way the architecture worked; does indeed use quite a lot of computations on a modern PC.

The current ones that I still use are:

Dolphin (v4.0.2)
*Libretro (Frontend RetroArch)

Cores used for Libreto

bsnes 0.93 Accuracy
PCSX-ReARMed r19
Mednafen 0.9.28
Stella 3.4.1
FCEU 98.13mm
PicoDrive 1.81
Final Burn Alpha 0.2.97.28
DeSmuME SVN
DOSBox SVN
Mupen64Plus 2.0-rc2
PPSSPP
Yabause