As others mentioned, SDL can be used to handle input in a platform independent way. It also has DirectDraw-like blitting and can support OpenGL rendering (though mixing them generally results in slow rendering -- better off using OpenGL directly to do the 2D if you need it).

For network related stuff, if you want something higher level than BSD style sockets (which, if used carefully, can be pretty cross-platform already between Win32 and most UNIX like systems), check out HawkNL:

http://www.hawksoft.com/hawknl/

HawkNL gives you functionality similar to DirectPlay and DirectVoice, but in a multiplatform open source package.

SDL + OpenGL + OpenAL work very well together, SDL provides you with your DirectInput equivilant, Threading, Timers, 2D graphics etc, OpenAL provides you 3D sound, OpenGL 3D graphics. As for directplay who needs it? good old plain sockets are far more powerful and almost 100% portable, you just need a few #ifdefs to select the appropriate headers depends on OS