When I was a kid, I loved Scrabble. Still do. You can play with 2 to infinity players. If she likes to read, give it a try.
We also did Monopoly, which honestly, I think is slow and boring. But many people love it. You can play that with 3. And there are now versions like "Animalopoly".
Yahtzee - I THINK you may be able to play with 3 (can't remember from my childhood & we are still at the Candy Land stage in my house). But it will say on the box. They still carry that at Target and Walmart.
Trivial Pursuit also probably has a kid's edition. That can be played with 3.
I think Operation can be played with 3 as well. I loved playing that one! Though I think my parents must not have since I ended up just getting to play "With" it.