If "failed terribly" means wasn't popular in the US gamer's home, then Wonder Swan, Saturn, and Neo*Geo were failures. But all three were at least moderately successful in Japan. The Neo*Geo was a failure in homes due to the high cost, but a success in arcades with it's ability to play multiple games in one cabinet.
Other notes:
* NUON isn't a gaming system, but a techology meant to augment DVD players. VM Labs erroneously tried to market it as a gaming technology, and at the time the demos were first generation PSX at best.
* The Sony handheld kennyb27 is talking about is the PocketStation. About the same size as Sega's VMS, it had a 32-bit (!) processor and i believe it played games directly off of a PSX memory card.
* i don't know if it counts, but Sega released a Genesis/Sega CD hybrid called the CDX. Basically it was a bulky CD player, or a compact Sega CD, depending on how you look at it. Then there was the Nomad...
* The Genesis 3 was released (and maybe designed) by Majesco. The main differences between the Genesis 2/3 and the original was the smaller size, and the omission of the headphone jack (and some other outputs i can't remember offhand). The Genesis 2 was compatible with the smaller Sega CD 2, and the Genesis 3 lacked the expansion to connect and of the Sega CD models.
* Sega also had plans to release the first VR headset (Sega VR), but numerous setbacks (like the number of people who got sick from using it) kept it from seeing the light of day.
* The TurboGrafix-16 handheld was called the TurboExpress. It was bulky but it had the first active matrix screen and played the same games as the TurboGrafix-16.
* The Neo*Geo CD was a terrible failure (as was the Hyper Neo*Geo 64). The NGCD had a single speed drive, and games often took 15-30 seconds between screens to load. It was about the same size as the Xbox, but twice as heavy. i had one for a while, but couldn't deal with the ridiculous load times.
* The Korean handheld the GP32 could be considered a failure, despite the fact that games are still in production.
* Sega had plans to release a Zip drive add-on for Dreamcast. Sega also planned to release Dreamsong, a karaoke-capable Dreamcast. i don't know if this was ever released.
* i'm sure everyone's forgotten Infinium Lab's and the Phantom, supposedly due to be announced this month.