The main requirement is a port of libsdl for your system. DOSBox should compile on every system with a decent C++ compiler like GCC.
Minimum requirements for Win32 port to run are minimum requirements for Windows 9x and SVGA card. But system requirements for smooth gaming depend on the requirements of the concrete game and the hardware choosen to be emulated in DOSBox.
Protected mode games are more resource-demanding. Although they will likely run on a 1 GHz machine, it is unlikely they will run quickly or smoothly. Be sure to read the sections on special function keys used by DOSBox, and how to run resource demanding games.