I am basically the only one in my family besides my uncle who plays Zelda. My immediate family doesn't play any video games, and my cousins are all super into Pokemon. Sure, I love playing Pokemon with them, but they don't really seem interested in Zelda.
My oldest brother plays Zelda. He's the reason why I'm even into it as he had the original on NES. Growing up, I've watched him play some of the others until I started getting my own consoles and games. My older sister isn't much of a gamer but she loves Zelda too.
Nobody in my immediate family plays Zelda. It's quite sad, actually. My extended family on my step-mom's side, however, is full of Nintendo Gamers. My stepbrother and stepsisters are even bigger Nintendo nerds than I am! I love it when they visit because it actually means I have people I can play Smash and Mario Kart with (aside from online). Other than them, though, nobody in my family is interested in Zelda or Nintendo.
At my university, though, I have several friends who are Nintendo fanboys.
The reason that my older brother and I became introduced to the series was because my Dad played it. I have fond memories of all three of us (my Mom's more of a Mario fan ) huddled around the TV solving puzzles and beating dungeons. I'm definitely more obsessed with Zelda than anyone else in the family, but my Dad still plays when new games come out, and my brother and I occasionally have Zelda marathons together.