What I like to do is listen to really sparse music and learn from it...
What works for me sometimes is to record more and then get rid of stuff, that way you end up with non-overplayed parts.
Practically speaking, you can do melody/harmony lines on instruments instead of chords, have the drums with no cymbals, or use a thin rimshot or a creative noise instead of a big snare on some songs.. turn the drums down to give other stuff more space, don't double track anything, have one guitar part instead of a million and say no to overplaying.
What also helps me is to overdo on the effects as I record, that helps me to play less. Put lots of delay on electric guitars and play fewer notes. Lots of reverb on other stuff so you "feel" the space AS YOU record.. anyway.. just ideas.