These were all toys that my daughter loved when she was 1, so I believe they would make great gift ideas for other 1-year-olds as well!
1. SoapSox
These lovable plush buddies can be taken into the bathtub and work as washcloths! Our daughter has the turtle and hippo that she received from her grandma as a gift. She loves playing with them in the tub and outside in her pool too!
You can find other SoapSox characters on the SoapSox website: www.SoapSoxKids.com
2. Mega Blocks
Mega Blocks are a great STEM toy! We actually got a bag for our daughter's first birthday. She didn't really get into them till closer to 18 months when she figured out how to put them together herself. Before then she mostly just smacked them together or handed them to us to show her how to make something.
3. Toy Cars
One of our daughter's first words was "car" and she loves playing with them! She learned how to "vroom vroom" quickly, so it's a great way to teach them how to make sounds too! Her favorite one is the Oball car (pictured below), but she also has a Mega Blocks train set she likes and a few other random cars.
4. Bead Maze
We got one of these from a family member and our daughter loved it. It's another great STEM toy. There are quite a few on Amazon in various price ranges, but here is one that is similar to ours for under $20:
5. Balls
We got these before our daughter was one, but she mostly chewed on them as a baby. It wasn't until a little after turning one she actually began to roll them and practice throwing them. The Infantino balls are great as they also have fun textures.
6. Shape Sorter
I can't find the one we got anywhere so I'm thinking it's no longer available. It's a cute barn with animals that have shapes. I believe it was Infantino brand. Our daughter loved chewing on the animals a baby. She still does now as well at 23 months, but she has shown more interest in trying to push them through the shape holes in the top of the barn. There are many different ones available now, but here is what a simple one looks like:
7. Phone
My mom actually got our daughter both of her phones as presents. She has the classic rotary telephone and a cell phone one that makes noises when you press buttons. Luckily it's not very loud and it does have an off switch! She was more into the noisy cell phone at first, but around 20 months or so, she really started loving the telephone. We think it's because she figured out how to pull it using the string and now she loves to drag it around everywhere!
8. Wooden Blocks
I originally got a bunch of these from Target's dollar spot for our daughter's newborn photos as I wanted to spell out her name. We let her have them to play with when she turned one as it was a great way to get her to practice stacking! Her favorite game now is to build a tower as tall as she can before it falls over. Such a great STEM toy.
9. Puzzles
My mother in law got our daughter this farm animal puzzle. It's suggested age is 2 and up, but our daughter still liked playing with the little wooden animals. She even started trying to put them back in their place around 18 months. She's gotten even better now at 23 months. However, they do make puzzles geared for 1-year-olds like this one: