The shape-changing concept where objects reconfigure their physical geometry has the potential to transform our interactions with computing devices, displays and everyday artifacts. Their dynamic physicality capitalizes on our inherent tactile sense and facilitates object re-appropriation. Research both within and outside HCI continues to develop a diverse range of technological solutions and materials to enable shape-change. However, as an early-stage enabling technology, the community has yet to identify important applications and use-cases to fully exploit its value. To expose and document a range of applications for shape-change, we employed unstructured brainstorming within a public engagement study. A 74-participant brainstorming exercise with members of the public produced 336 individual ideas that were coded into 11 major themes: entertainment, augmented living, medical, tools & utensils, research, architecture, infrastructure, industry, wearables, and education & training. This work documents the methodology and resultant application ideas along with reflections on the approach for gathering application ideas to enable shape-changing interactive surfaces and objects.