OK, I am going to start from the top, in my head, and assume you have a car, and may well overlap with others.
I have a self-catering/camping "kit" that I check for purpose (am I camping or an actual building? Will there be a dishwasher or washing machine, or not? Etc) - and take out what is not needed on that trip. But these things are specifically reserved for travelling, rather than used in my regular kitchen. Some are used and brought home (tools), some are used up and replaced when I get home (bin liners etc).
An Ikea chopping board (the small blue one as part of the 2 board set - I gave Cub Scouts the large one as the camping box there needed it 
)
3 decent knives, all with sheaths to protect fingers when rooting around
a set of Ikea nylon cooking tools - spatula, whisk, ladle, serving spoon
2 wooden spoons
Can opener
Corkscrew
Vegetable peeler
Set of silicon oven mitts
100ml squeezy bottle of washup liquid
1 pot scrubber
2 new J cloths
1 washing up brush
1 tea towel
1 Ziploc bag containing 7 dishwasher tablets and 3 double packs of washing up powder tablets
Handful of clean pegs (to close packets and to hang things to dry)
Couple of clippits as well to close packets
1 each glass mill for salt and pepper (the kind that are a glass jar from the spices aisle with the mills in their lids)
250ml bottle of olive oil (that I refill at home)
2 bin liners
2 toilet rolls
roll of cling film
roll of tin foil
3/4 Ziploc bags (for saving leftovers/marinating meat etc)
Box of matches
Couple of nightlight candles
few spare batteries
Pack of cards
Couple of pencils and pens, small notepad (usually from beside the phone in hotels)
Chalk (useful in Centre Parcs)
I also bring a couple of travel games, monopoly or similar, and a handful of DVDs if there is a player (car, laptop, or in the accommodation).
Charging cables for any electronics etc, and adaptors.
I have lots of torches anyway, so tend to throw in a couple of head torches for darker evenings. Some places are not terribly well lit.
If I think there is no coffee plunger in the accommodation, I will bring my plastic one for camping.
If going to France, I bring some squash, as they don't have the same kind of thing (Sirops are nice but different, and sometimes you just want squash)
Barry's tea (the only similar is Liptons, and not always available)
Enough coffee for 1st 2 days
Proper butter
Some one of these years, I will remember to bring a mug from home, but I now have a collection of them from French supermarkets.
If driving and you have space, a coolbox and iceblocks may be useful. The fridge may be small in the accommodation. And you may want to bring things for the journey or a 1st nights' meal, and perhaps want to bring home some nice cheese or fresh produce.
I've also learned to either bring or prepare to buy sheets and towels. We paid for sheets and they were the papery disposable ones that don't last a fortnight - but the sheets in supermarkets there are actually relatively cheap.
French pillows are square and not great - if you have room in the car.
Camping towels take up less room than regular towels, work well to dry you off (slightly different technique) and are quite quick to dry again themselves, but are also, if you get the larger sized ones, they can be useful as extra blankets if necessary. Decathlon sells decent ones, and may be local to your accommodation - check their website as something you could take home to replace things you use up while there.
(Decathlon is also great for sun hats, sun glasses, water shoes, extra tshirts and shorts, camping gear, and all sorts of sports and outdoor gear). Or a football if you don't bring one.
Check the rules in your accomodations about BBQs and fires - some allow them, some have designated areas, some don't allow them. If they are allowed though, it might be useful to bring one from home if there are a lot of you and you have space (a travel one, or one that comes apart for transit).
Also, if there are a lot of you, possibly bring 1 large pot (or buy in the big 1st shop) for pasta etc as the pots and utensils tend to be just sufficient for the van. It can always be filled with towels or tshirts or something in transit.
A small backpack or day sack for use out and about - carrying water and money and snacks if you go out for the day, or if you get bicycles. And handy to bring back small amounts of shopping on foot or by bike.
Sunscreen if you use high factors, as FR tends towards lower numbers (getting better but....) or DCs need solid sticks or specific brands.
Bug spray or wipes.
First aid kit:
Antiseptic wipes
Band aids
1 crepe bandage
1/2 larger dressings
Pain killers
Antihistamines
Any family meds
Scissors and tweezers
I tend to go with a fair few bits and pieces, and expect to go to a large supermarket on that 1st morning after arrival, for food for a few days, and usually a few other things (like the last time it was sheets (paper versions we'd paid for were not going to last), a couple of mugs, and a corkscrew as we'd forgotten that). Some of those extra things may come home with us if useful and we have space, but I am prepared to leave them behind if necessary.