Some of the examples above have indeed shaped whole "disciplines" but others, as striking as they are, are less sweeping in scope.
For me, a very important and thought provoking example, and historically important for a variety of reasons is the Tutte graph. This graph shows a 3-valent 3-polytopal graph which has no hamiltonian circuit. This example, in particular, doomed attempts to prove the 4-color theorem based on ideas related to hamiltonian circuits.
It inspired a great variety of conjectures and work related to hamiltonian circuits for polytopes.