Sega Game GearBefore the rest of the world had ceded the handheld market to Nintendo (who have a 99% market share in 2001), Atari, NEC, and Sega all tried to knock the GameBoy off its lofty perch. The funny thing was each one of the GameBoy's competitors blew Nintendo away in terms of computing power, but to one degree or another there was always some important aspect of handheld gaming that was overlooked. In all three cases, battery life and size were major obstacles that couldn't be overcome.
The Game Gear still had a fairly long life, first going on sale in 1991 before support was completely dropped in 1997, then being resurrected by Majesco Sales in 2000 (I'm honestly not sure of the current status - all I know is the Toys 'R' Us stores by me do still sell the Majesco version, though that may just be back stock). Really nothing more than a portable Master System with a different cartridge slot, the Game Gear had a bit of an advantage over both the GameBoy and the Lynx in that developers could easily port their games from the home console to the Game Gear simply by burning their ROMs onto new cartridge wafers. Eventually, an adapter called the Master Gear converter allowed gamers to play actual Master System cartridges on their Game Gears. (The reverse was not possible, as the Game Gear actually has a larger color palette than the Master System.)
The Game Gear did have some limited success in the marketplace, but it never even approached the GameBoy in terms of sales. Holding the system back was a very short battery life (around three hours, though Sega's official specs say over five), and quite a bit of bulk - almost as large as the Atari Lynx, it's also about double the weight. Sega did all they could to support the Game Gear and in fact it ended up with a nice stable of around 350 games all told (Game Gear-specific and Master System games), plus some nice peripherals like the TV Tuner to go with its full-color screen. In the end, though, customers wanted simplicity, light weight, and long battery life - all things the Game Gear did not offer.