I like to buy my nieces books, because they have enough clothes and toys already. Unless they MUST have those plush Frozen dolls, then I give in. But for my 1.5 year old niece who can't tell me what she wants, I bought her 2 books, Sophie's Squash by Pat Zietlow Miller and The Gruffalo by Julia Donaldson.
I learned about Sophie's Squash in my writing class. There was a lot of hype for this book, especially for a first time author. We had to get our hands on it, so finally someone found it at the library and we passed it around in class. It's a really cute story about a girl and her pet squash. She takes the squash everywhere and gives it a name. And as you know, a squash wont stay a squash forever. So she lets go of her squash, and at the end something amazing happens. This book won the Golden Kite award, you can see it here: http://www.scbwi.org/2014-golden-kite-winners/.
The Gruffalo I heard about when I was in Germany visiting my brother. It's extremely popular in Europe, so popular they made a cartoon show that my nieces were obsessed with. The author has several books and all have done really well. The Gruffalo sold 12 million copies, which is unheard of for a children's book! It's about a mouse who gets approached by several animals in the forest who want to eat him. But he tells them it's not a good idea, because he's about to meet the Gruffalo, a scary creature he made up. Then the mouse actually does meet the Gruffalo, and the Gruffalo wants to eat him, but he says that is not a good idea, because all the animals in the forest are afraid of him. And he back tracks through the same animals he meets in the beginning. Really fun story, highly recommended.