For me it’s the Gizmondo. At a time when handheld gaming was the Gameboy (or my runner up in this very category the Nokia Ngage), the Gizmondo promised graphics well ahead of anything on the market - 3D graphics, mobile online multiplayer, GPS location based gaming…
I eagerly purchased one at launch for about £500, despite there being no real games available. There were promises of exciting by options including a Jenson Button branded racing game, and a 3D turf war game that uses your actual real world location to create boundaries and areas you control.
It was more than just a gaming device though, offering the ability to send and receive SMS, although no phone calling, and it could even be used as a sat nav device long before smart phones and apps were a thing.
Sadly the project was one of the biggest flops in technology history, with the founder being investigated for criminal activity, and the company going bust a few months after launch. There are some great YouTube videos about the whole saga here, from glitzy celebrity studded launch parties to burned out supercars, so instead of doing an inferior job of explaining the whole story I will share a link below so you can give these folks the well deserved views.
Despite the fact its potential was never realised, the Gizmondo has a fondness in my heart, and a permanent placement in my gallery of gadgets alongside my Barcode Battler and Nokia N-gage QD (the non-taco version).
Edit: Added photo of the relic sitting on display