I use KiCad; other popular ones are Eagle (though they have recently changed their licensing and have limitations), and Diptrace. I would stay away from ones that lock you into a specific vendor (ie. ExpressPCB). I haven’t used the free Eagle or Diptrace so I don’t know how well they work for multilayer. KiCad can handle up to 32 layers with planes or pours on any of them.
Sparkfun supports libraries for KiCad and Eagle, so if SFE is one of your preferred sources for components you may want to stick with one of those. Adafruit and Pololu favor those as well.
I use pcb-rnd and sch-rnd. These are part of the Ringdove EDA suite. A lot of ex-gEDA users are migrating to Ringdove these days, now that gEDA is dead.