D.D.
My kids love Minecraft. It's the only app I've ever bought for them. Think of a big electronic lego set, and that's minecraft.
Here are some free apps they like:
fruit ninja
flow free (puzzle solving, you can get all levels, and I like it too)
where's my water
they used to love angry birds, but they are mostly past that one
I also have a bunch of educational ones. I search 'free toddler' or "free 2nd grade math" or something like that, and see what I can find. I have a bunch of apps where you touch the animal and it makes the sound, or you have to identify the animal. And a toddler shapes app, where the child has to identify the shapes to get electronic stamps. I also have some book apps, where the book reads itself and has some associated games. I'm not sure of the exact name, sorry, I found them just by searching free toddler apps.
These are on iTunes, but I'm guessing Google Play probably has a lot of the same apps.