AC system: Not sure if Nest does this, but remote control of the system when you are coming home early (and it is 107F outside) and the temp isn't set to lower for another few hours. Health monitoring so you can spot a problem and call the repairman before it is 95F in the house and you just got home.

Stove/Crockpot: Change the timer so that the cooking time starts earlier or higher temp so the food is cooked sooner. Adjust the timer on something like a bread-making machine to start earlier/later depending on a schedule change.

Irrigation system: Modify the timers while out of town to account for any weather changes/rain.

DVR: Notification that you ran out of space and are not going to get the show recorded you were waiting for. Delete shows remotely to free up space (Myth TV probably does that already).