phone. You can ask the phone co to block outgoing calls to overseas or premium rate numbers before the leaving date, or set it to incoming calls only if you want, then you can keep it going until you walk out of the door for the last time. They normally close accounts at midnight. You can unplug and take with you the phones to prevent the moving men using them.
any garden ornaments or favourite plants (take cuttings)
unbolt the safe, or at least take your money out of it
all banks and credit card companies
Car insurance
Make sure sure Home and Contents insurance covers your new home from 00:00 on the day you start to own it; and your old home up to 24:00 on the day you cease to own it. Tell the new owners who the insurers were in case there are arguments about damage or subsidence or something.
your employers; pension co; national savings if you have any; company registrars if you have any shares; inland revenue; the state pensions office; anyone who might pay you benefits; any companies where you have a product still under guarantee. TV licence. Council tax as you might get a rebate.
subscriptions to clubs, magazines etc
change of address cards to friends and realtives (or do a standard letter on the PC)
get a bank statement/cheque book and look at all the people you've paid recently to check they're all notified. A letter is more reliable than a phone call. Remember that some are paid quarterly or annually.
The post office will fail to forward some items, leave the new owners some large, stamped addressed envelopes and ask if they would be so kind as to forward anything that turns up. This will especially happen at Christmas and birthdays. Pay the Post Office for a whole year's redirection. You can also get them to hold mail for a few days if there will be a gap between moving out and moving in.
Take with you new padlocks and hasps for garden gate, shed etc (if any) and at the very least a new cylinder for the front door
If you have a particularly expensive door lock, or suited keys like me, or have had lots of spare keys made to suit, take them off and put a standard one on. Make sure you leave the new occupiers all the keys to back door, windows, shed, gate, patio doors etc (they're no use to you any more). Also leave them labelled cans of paint in the shed for touching up or repainting. If you are fond of gardening you can leave them a chart showing what's where.
Take with you your DIY tools; toilet roll; soap and towels; teapot; kettle;
toaster; uht milk; sugar; torch; light bulbs etc where you can get them all out without having to unpack everything else. Also vacuum cleaner bin bags and household cleaners as some people are pigs.