Whenever I have someone stay over they are always amazed I don’t have certain things they are never out of.
Things people ask for that I don’t use:
olives
olive oil, much less extra virgin olive oil (I use whatever’s on sale, canola usually)
mayo
balsamic or tarragon or any flavoerd vinegar
marischino cherries
cooking sherry
cream cheese
whipped cream or substitutes
rye bread
No sugar
No olives
No olive oil
Mayo, but no bread
No vinegar
No maraschino cherries
No cooking sherry
Cream cheese (for English muffins, bagels)
No whipped cream
No rye bread
No milk, unless I specifically need it for a recipe.
How can someone live without olive oil? Much less cook without it?
I use bacon grease.
Things we very rarely have in our kitchen these days:
Milk
Potatoes
Bread (The occasional bag of buns or loaf of sourdough will appear every now and then.)
Same here. I just don’t like milk, but olive oil? Sheesh, I couldn’t live without it! I always say: give me a little garlic and some olive oil, and I can cook anything!
No pork products (obviously).
I don’t keep olives on hand- if I want olives, I get good ones from the olive bar at the grocery store, and use them quickly. No jarred or canned olives for us.
Celery- Mr. Neville doesn’t like it, and can taste really small quantities of it, so we don’t use it in our cooking.
Most bottled salad dressings. I have some ranch, blue cheese, and honey mustard for dipping sauces, but usually when we want a salad dressing we make it ourselves from oil and vinegar.
No milk that is not fat-free, and no half-and-half or cream.
No dessert stuff, other than the obligatory Girl Scout cookies and Passover desserts- Mr. Neville and I are fat enough without desserts, thankyouverymuch. That means we don’t have maraschino cherries or whipped cream.
Cooking sherry or cooking wine- when we want to use sherry or wine for cooking, we use regular drinking sherry or wine.
White vinegar- we always use balsamic, sherry vinegar, or rice vinegar.
Pancake topping- we almost never make a sit-down breakfast.
Decaf coffee- I’m the only one who drinks coffee, and I know decaf for the abomination unto God that it is. We had a can of it for a while (bought for a visit by my parents), but it lasted for years, until we threw it out when we moved.
We have butter, but it’s in the freezer- we pretty much use it only for cooking, not for spreading on things.
We might very occasionally have parve (non-dairy) margarine to use with meat recipes, but we don’t have any other kind of shortening.
We don’t keep potatoes around- I had a bad experience with forgetting about a bag of potatoes in a cabinet until I found them all full of maggots.
We have mayo, but rarely use it, and don’t use it for spreading on stuff- it’s almost always for making aioli. We don’t have Miracle Whip, because that stuff tastes like mayonnaise six months past its expiration date (and I would know).
Potatoes.
We rarely have potatoes around, unless I specifically need them for a recipe. As in, Christmas and Thanksgiving, mostly.
Eggs: Well, technically we usually have a couple somewhere in the back, usually at least 2 months past their expiration date. We simply don’t cook and eat them very often, and we don’t often bake or make other recipes that call for them.
olives
marischino cherries
cooking sherry
cream cheese
rye bread
brown sugar
Crisco
Peanut butter
Alcohol
A lot of the stuff you guys are listing I don’t consider particularly common to begin with. I wouldn’t surprise me to find that someone doesn’t have maraschino cherries, decaffeinated coffee, or rye bread. Some people like them but it’s far from a huge crowd.
I don’t keep a lot of potatoes around myself. I didn’t use many to begin with and a five pound bag sprouts and starts burning off its starch before I finish them. And that makes me even less inclined to use potatoes.
Same problem for dairy (other than butter); I buy small amounts of milk, cheese, or cream when I need it.
I try to buy produce the day I use it so unless it’s something that keeps (like onions) my fridge doesn’t have a lot of produce in it.
My list on not-on-hands:
olives
decaf coffee
meats - I buy fresh if I need it
texas pete (or other brand)
wine
vegetables - again I buy as needed
fruit - buy as needed
bread
equal or sweet-n-low (yuck!)
margarine or non-butter spread (Only real butter in this house)
Bread(half of it always goes to waste)
eggs
coffee
meat(only buy it occasionally, and use it right away)
olives-- I just don’t like the flavor
cooking sherry
mayonnaise
honey
hot sauce
bacon
I don’t even remember what’s in my kitchen . . . except for bacon salt (all 3 flavors). 
Pork
Wine
What I find interesting is how many people list “olives”. I hate olives, but I thought I was unusual. Olive oil, yes. Olives? No thanks.
Ketchup. I loathe its very existence.
White bread.
Iceberg lettuce (it’s just crunchy water, people!)
I don’t normally keep alcohol in the house- I don’t often drink here, I usually go out to bars or to friends’ houses, so they get any leftover alcohol.
Whipped cream
Margarine- I try to avoid trans fats, thankyouverymuch.
Cookies. Sometimes I’ll buy Nilla Wafers, but that’s it.
Ice cream or other dessert-y items. I eat fruit and yogurt instead.
I do have maraschino cherries for my occasional whiskey sour.
I neeeeeed olive oil, I don’t know what to do without it.
And one uncommon item I always have is tahini. You never know when you need to make hummus.
Move to Qatar you can have wine…no pig 
Hmmm, things people would think I have in my kitchen but don’t:
Crackers
Cookies
Snack chips of any kind
Candy (just 65% or more chocolate, which none of my guests want!)
Soda
Microwave popcorn (I only air-pop)
Milk (just soy)
Maraschino cherries - I didn’t know those were a staple!
Mayonaise
Bread
Olives - I didn’t know those were a staple, either! But lots of EVOO
I do have dried fruit, almonds and walnuts on hand, and high fiber cereal to go with the soy milk. Whole wheat pasta, wraps, veggie burgers, canned beans and tomatoes, apples, garlic and onions are staples in my cabinets and fridge.
Usually a guest’s stay begins with a shopping trip to get them food.
I was afraid I was going to be the only one in this thread to confess to a ketchup-free kitchen.
I don’t keep much of that on hand, but I loves crunchy water. (Yes, I do eat ice. Lots of it.)
But but but… that’s one of the four food groups! The flavor group! 
To continue with the spirit of the OP -
olives (when did they become normal, though?)
honey
cooking wine (No objection to it, just haven’t picked up any, lately)
sliced cheese
white bread - for that matter most any form of pre-baked bread.
Rosemary
steak sauce
OJ