The pony:
Pony,
Saddle,
Bridle,
Spare bridle,
Bit,
Reins.
Stirrup leathers and irons.
Spare rubbers for peacock irons.
Girth.
If you have a white pony/girth, trainer whitener is very useful for those annoying grass stains!
Travel boots,
Travel rug
Waterproof sheet incase it rains.
Hood if required,
(I have a snow white pony, ALWAYS required)
Tail bandage and the leg of an old pair of tights to go over the tail.
Head collar,
Lead rope.
Grooming kit, newly washed.
Hoof pick,
Sponge,
Bucket
Shampoo
Show sheen
Chalk for white bits
Hoof oil
Baby wipes
Baby oil for muzzle and eyes.
Haynet
Water bucket
First aid kit.
Poo picker,
Bag for picked poo.
Water.
Baling string to tie up to. The string you always use will definitely break at the earliest opportunity.
Rider:
Normal everyday riding clothes to wear there and warm the pony up.
Show kit: jodhpurs
Loose trousers to wear over jodhs between classes
White shirt, spotlessly clean, they MAY let them ride in in no jackets if it is sweltering, dont be embarassed because you thought the slightly grubby school shirt would be covered by the jacket! 
Tie
Tie pin
Jacket
Joddie clips (or elastic sewn directly to the jodhs)
Hairbrush
Hairnet
Hard hat
Well polished boots
Boot polish
Safety pins and scissors for the competitor number
Gloves
Show cane
Body protector
Rain mac
Wellies
Deodorant
First aid kit
Baby wipes
Lunch.
Most importantly, in this weather, every empty bottle you can find, filled with squash/water and then frozen. Take than out in the morning and put in a bucket which you can later fill with water. It's VERY easy to overheat and get dehydrated at shows, when you are wearing show clothes, these will slowly defrost through the day, keep you cool, and give you a bucket of iced water to put to good use.
Whatever you do, put EVERYTHING you will need on your list. You may think that boots, stirrup leathers and saddle cannot be forgotten, but believe me, it's very easy! And that includes DD! 
Once DD is changed into show clothes, don't let her stand ANYWHERE near the car/lorry/trailer, she WILL step over the tow bar and get covered in grease!
If you are in two very close together classes, STILL remove the bridle and tie up with the head collar. If you don't, your pony WILL despite never doing it before, pull back and break its bridle in six different places.
Do not EVER tie your spotless pony next to its best friend for company. A friendly neck scratch WILL result in you frantically sponging it down, trying to remove large patches of grass coloured slobber from your white ponies neck and mane!