I went into Edit - Project Settings - Input and removed arrow keys from horizontal and vertical inputs (only keeping WASD keys). After I build stand alone app, the input mapping is lost, and strangely, horizontal and vertical inputs were set to all arrow keys without WASD keys (so different from default mapping too). The web build is find and I have the correct mapping.
The computer I am using is Windows 7 64bit, and Unity editor version is 4.1.5f1.
The funny thing is when I used a Windows 8 64bit computer with same Unity editor version 4.1.5f1 and built the same project, everything worked correctly.