Depends on the weather and how much I'm carrying. For most trips I go on (fair weather and light loads), pretty much everything gets hung or placed on the ground under the hammock.
My pack sheet (now empty; odd pack design) gets hung from the foot end. My day pack/water carrier (told you it was an odd pack design) gets hung from the head end with my thermometer clipped to it (more weight in that, so it pulls down harder on the suspension, and I want the head end lower than the foot end). My food bag gets hung from a branch, PCT-style, at least 100 yds from my site. My tarp is over the hammock (usually rolled up in its Velcro keepers, snakeskin-style, if the weather looks decent). My insulation is in and on the hammock (if above 50* F for the lows, I'm using my poncho as the main under insulation here, holding a crumpled space blanket; otherwise, the poncho goes underneath as a groundsheet). Any extra clothing I've brought is in the oversized blackbishop bag at the head end (usually just a shirt and socks on short warmer trips, sometimes undies if it's a longer warm trip). My headlamp and watch get hung from the SRL. My shoes go under the hammock unless it looks like serious rain (if it does, they get hung from the SRL). My ditty bag goes on the ground under the hammock unless it looks like rain (then it also gets hung from the SRL). My bike or hiking poles get left on the ground near the hammock. And that's it for gear for me.
Hope it helps!
"Just prepare what you can and enjoy the rest."