Make sure you provide your new address to the house owners (if you rented it) or to its new owners (if you sold it) before moving. This way if your mail or bills come in, they would know where to find you. Of in case you forget some stuff, they could mail it over to your new location.
Make sure you cover all the bills and if any remain unpaid or undue, notify the post office and redirect them to your new address. This is a sure way to avoid any possible conflicts.
-Chemicals and stuff
You may keep some paint or opened cans and jars with chemicals, building materials, poisons, etc. Make sure you dispose of them in a proper and eco friendly way. Send them for recycling or give away to someone who could benefit from them. Do not attempt to move opened cans, as it may end up in a disaster.
-Clean up all the corners
There are many corners around the house which may not regular cleaning. They might be hard to get to (hiding behind your furniture or appliances). Make sure to clean them well after you move those out.
-Make provisions for pets
If you have pets, you should clean the house of what they could leave behind and make new arrangements for their wet care and other needs in the new town or city.
-Turn off electricity, gas, etc.
Even if the house would stay empty for just a couple of days, make sure to turn off all the water, electricity, gas, etc. You do not want any damage done to it when you are gone.
These simple hints would allow you to prepare for a safe and stress free relocation. Use them for your good and make a checklist for things to do.