Generally speaking, I recommend utilities be turned off either the day of the closing (if the utility company's policy is to do so after 5 PM) or the day after (if the utility company can't give a time of day they'll be turned off).  You always want to be sure they're on during a walk-through, which is sometimes scheduled for the same day as the closing.

Frank, unless there are unusual circumstances it would be day of closing.  The importance thing is for both parties to call at least four business days ahead of the closing to make sure the utilities can get out there.

I usually recommend a final reading the day after closing.

Keep the utilities on until after the settlement is completed and title has transferred. Use the same guide for the insurance policy. 

I ask my seller to schedule turn off 1 day after closing.  I email the buyers agent all the utility company contact info and remind them when the seller is having the utilities cut off.  I do this after due diligence.

On the day of closing.

I like a seamless transfer of utilities. I start a couple of weeks before closing notifying the buyer or buyers agent to get them ready to turn over day of closing. I remind again at the walk through and again at closing. If I am representing the seller I tell them to check the day after closing to have them turned off even if the buyer has not transferred.