Atari 2600 - the console that started it all
It wasn't the first console, but it was the first to be successful. And it is still alive.
The Atari 2600, originally called VCS, was my first game console. Officially produced for almost fifteen years (much longer, considering eastern fakes), the machine was one of the first consoles to use a cartridge as a game carrier. Perhaps, as the first one, it used the 6502 processor (or rather, its trimmed version - 6507).
It only had 128 bytes (yes, bytes) of RAM. The graphics chip allowed to generate graphics with a resolution of 40 x 192 px, although an efficient programmer was able to squeeze 160 x 192 px.