The physical property investigation (like transport measurements) and ultimate application of the topological insulators usually involve surfaces that are exposed to ambient environment (1 atm and room temperature). One critical issue is how the topological surface state will behave under such ambient conditions. We report high resolution angle-resolved photoemission measurements to directly probe the surface state of the prototypical topological insulators, Bi(2)Se(3) and Bi(2)Te(3), upon exposing to various environments. We find that the topological order is robust even when the surface is exposed to air at room temperature. However, the surface state is strongly modified after such an exposure. Particularly, we have observed the formation of two-dimensional quantum well states near the exposed surface of the topological insulators. These findings provide key information in understanding the surface properties of the topological insulators under ambient environment and in engineering the topological surface state for applications.