Basically everything that is not a danger hazard (cutting. chocking, burning, toxic...)
One-year old just love copying mummy, the love stacking things, piling them, banging them, trowing them from the high chair and see how they fell...
So:
- cups, plastic pots, pans, wooden spoons
- empty boxes
- shoe laces (short enough so they can't go round their neck)
- brushes (nail brush, dish brush)
At this age, my son favorite (over any toy) was an empty water bottle!
Still today, at 2 1/2, he likes to play bowling, meaning arranging 6-9 empty, clean yogurt jars on the floor and roll a rolled pair of socks over them and knocked them off!
You can create maracas by having sand/small stones in a empty small bottle (glue the cap) or into 2 jars of yogurt glued together.
To play textures, you can have small stones, sand, cotton balls, foil paper... into socks and he can play with them and try to recognize what's inside.
When folding the laundry, socks also make great puppets.
Hide a small object (not too small to avoid chocking) somewhere and let him find it (again a empty yogurt jar, for example). Its easily hidden behind a chair feet, below a pillow or blanket, behind curtains...
Little ones also like to collect "treasures" from the park that you can play with, invent stories from, or later use for art projects: leaves, feathers, small stones, wood sticks, snail shells, dry fruits, pine cones.
Have fun!