Being the middle child, I shared different gaming consoles with my brothers: A NES, SNES, Sega Genesis, N64, and PS1/PS2. The very first game that I had was Mario Paint for the SNES though I'm not sure that really counts as a game since it was more of art application.
However the first gaming console that I owned myself was the Gameboy and my first game to go with it was Super Mario Land 3: Wario Land.