Only requirement is a port of libsdl for your system. DOSBox should compile on every system with a decent C++ compiler like GCC.
The system requirements for smooth gaming vary depending on the system requirements for the original game, the desired gameplay experience, and the hardware being emulated.
Protected mode games are very 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.