Two of my major memories of learning objects are right here -- cuisenaire rods and tangrams! That's cool, and a fond memory for both.
Aside from Lego, which I've tinkered with since I was 3 years old, I think that "random stuff" had to have been my favorite object when I was younger. A couple of stand-out objects were the metal brush pieces from big mechanized street sweepers (I would find these when I went for walks with my mother because I was small and close to the ground), and capacitors from radios that I would take apart. Between things like that, some glue and some paint, I remember making all sorts of collages and art pieces that vaguely represented cities.
Most recently in the classroom, on advice from a colleague, I've been experimenting with shoeboxes, construction paper, ribbon, and other colorful objects with glue. The context is less about mechanical skill and more about reflection. In this case, it's a class about deign thinking and nutrition, where we are having middle school students represent "food they want to eat" on the inside of the box, and "food they are told to eat" on the outside of the box. Then they have an opportunity to explore the differences and potential challenges to eating healthy. It's been interesting to see how much real engagement the kids have in the physical activity, but also the sense of ownership in creation since it's both something they've made and representative of something in their lives.