The Bally Professional Arcade, also known as the Astrocade. Featured very true-to-arcade versions of Bally/Midway arcade games. The crown jewel of its library was The Incredible Wizard, the home version of Wizard of Wor. 1978-1983

The Atari XE Game System (XEGS), a consolized version of the Atari 400/800/XL/XE computers. However, it could be expanded into a computer with the full function of an Atari XE computer, with keyboard and disk drive. The Atari 8-bit line in itself shared its basic architecture with the Atari 5200, to the point where many 5200 games were ported to the Atari 8-bit computer, either officially or by hackers. Plus, it took standard Atari joysticks instead of the crude analogue stick that the 5200 was stuck with, and Genesis controllers would work with it because the Genesis has the same 9-pin connector for its controllers as Atari.

This video isn't the XEGS per se, it's the Atari 400 Mini, but it can be configued to any configuration of the Atari 8-bit, which includes XEGS and 5200 ROMs. One of my favorite A8 games was Donkey Kong, which was the most failthful home port of Donkey Kong released at the time. It was more faithful than Nintendo's official NES version.

The Texas Instruments TI-99/4A home computer. One of the world's first 16-bit machines, released in 1979. Started out with a library of games produced by TI and Milton Bradley, most of which were off-brand versions of popular arcade games like Pac-Man and Space Invaders, but it had a few unique games of its own. Later got officially licensed versions of arcade games from Atarisoft. It also had a lot of educational software, and even productivity/home finance software on cartridge. It also supported floppy disk and casette tape media (the tape would make a neat digital noise pattern as it loaded.). It also had a speech synthesizer which could say a number of words from a set vocabulary. Being 16-bit, it had a rather broad color palette for a late 70s/early 80s console/computer. Its downfall came when Commodore initiated a price war which made it impossible for TI to make the computer cheaply enough to compete, despite strong sales in its first year or two.

Why do I sort of need a controller like that in my life??

I looks awesome in a very crappy way. Love it. 

The most exotic things I've seen in real life are Sega SC-3000, Philips Videopac G7000 (European version of Odyssey 2) and ZX Spectrum home computer.

ColecoVision

Launched in '82, with motto of arcade-quality games at home, it not only did that, bringing arcade ports like Donkey Kong and Galaxian, but greatly influenced Famicom's creation as well. Arguably the actual start of 3rd generation (given that SG-1000 launched a year later with same hardware and it's considered 3rd generation). Killed prematurely by Coleco loosing faith in console market after the crash of '83 and focusing (unsuccessfully) on home computers (with ADAM, which ate into ColecoVision production line).

The Apple Pippin comes to mind. Apple seriously wants all memory of this flop dead and buried.

The FM Towns Marty, basically an Xbox 0 as it used an Intel 386SX CPU and an enhanced VGA GPU.

The Commodore Amiga CD³², basically an Amiga 1200 with an integrated CD-ROM drive and cartridge slot but no keyboard. It's the successor of...

The CDTV (Short for Commodore Dynamic Total Vision), a CD player/console that looks like a VCR and was based on the Amiga 500 and could be enhanced with a Floppy drive, Keyboard and Mouse to get all the functionality of an Amiga 500 for just twice the price.

The 3DO (for 3-Dimensional Optics), the first console with an ARM CPU and CD-ROM as main media format.

The WonderMega (X'Eye in the US), a redesign of the Sega CD as a standalone console with high-quality audio and could also be used for Karaoke.

The Casio PV-1000, predecessor of the Loopy mentioned above and notable to only have lasted mere weeks before being pulled from the market.

The Commodore 64GS, a C64 as a console without keyboard for the same price as the computer.

I think most older brits will be offended for calling the legendary Speccy forgotten.

A bit like spectrum the MSX always had a fanbase in Japan (5-7 million ) that people did not forgot but is even unknown in the West; Basically a Microsoft Project but with multiple companies making their own version (like Sony) it was the birthplace for some wellknown franchise (especially Konami) like Bomberman; Puyo Puyo and the Forgotten Metal Gear Franchise:

Zodiac Tapwave. Released in 2003. So, despite appearances, it's not ripping off PSP. It was a PDA merged with a game system. It had games that came on SD cards. Roughly as powerful as a PS1.  Like N-Gage, Gizmondo (another one on the list) and PSP, they took shots at Nintendo for being kiddy and this was for adult gamers. Sold about 200k. Marking it as a flop.

Gizmondo. Released in 2005. This thing is such a disaster from conception to behind the scenes, it could warrant its own documentary. From Carpet company to game console company to Swedish mafia. And a Ferrari crash that splits the car in hal,f and the Mob guy lived to tell the tale. It had two models. A cheaper $300 model with ads as you play. A proposed $400 model with no ads...the ads never happened. It had a GPS built in and a camera. Media functionality. It's best selling game...Sticky Ballz. Yup. Sold only 25K. Not as powerful as a PSP but could push about 1 million Polygons putting it above DS,Tapewave and N-Gage.