My first console was a PS2 with Die Hard Vendetta. It was a post-uni treat to myself. We had a binary household growing up, I was computers (Vic20, C64, Amiga, PC) and my younger brother was the console whore (NES, Master System, Mega Drive) and at uni my housemates provided a Playstation, SNES and N64 so I never needed to own one myself. Oh yeah, my grandparents had a Binatone pong system (with the paddle controllers) too.
It probably isn't a console per-se but when I was pretty young I owned two single-game battery/mains operated jobbies that had controllers and screen in one. One was a Caveman thing where you had to get up a mountain spewing lava and rocks (Donkey Kong rip off) and the other was a yellow PacMan one.