Here are some interesting things which can be built with agglomerations of equal-sized spheres. I got the yellow spheres from some surplus company some time after I started building models with toothpicks. Originally I glued them together with white household glue, but those models were very fragile. Later I used epoxy, but even some of those models have disappeared through the years with breakage.
The hardest to build was the icosahedron (front row, third from the left), but even that wasn't too bad once I learned to form two icosa caps first and then glue those together to form the final figure. The double helix in the back was the most interesting to assemble. It's complex and precisely linear appearance somewhat belies the ease with which it was put together.
It was really only by putting together these models that I intuitively grasped the correspondence between toothpick and sphere models of these objects. The cast of characters is: