I pull everything. All I send to the yard is a doorless shell that has to be dragged up the flatbed.
If you're limited to storeage space or time, then pull the stuff that wears out or is expensive.
I find it's the little stuff that saves trips to the parts store (window motors, hinges, dimmer switches, lights, fuel pumps, etc.

I even swapped a 92 Civic window motor into my wifes 00 CRV.

Where are you located? Someone may need parts. I'm currently looking for a red fenders and a hood.