Currently ours is 18"; our new custom cabinets will be 16".

Most sources I could find suggest that 18" is standard, but this is definitely one of those things that is open to some customization. We have 17 now and we are going up to 18, even though I'm short. I just like the appearance and functionality (in terms of counter usage) with more space, but others would rather have their upper cabinets be more useful. Whichever way you go, just make sure that any appliances you plan to keep on the counter (coffee maker, mixer, etc.) fit in the space.

With a coffee maker, flip the fill lid up and measure the height. Then add an inch.

Most often inspectors will use the specs from the range/cooktop for the cabinets on each side of it. That is typically 18". Often specified as 54" above the floor.
There are ways, depending on layout, to configure the rest lower. I use a minimum of 16 in those. My own is done that way to accomodate the short folks in the house. Cab on each side of srange at 18 rest at 16. Can be tricky to make work.
Occasionally some are done higher-21 to a maximum 24. Usually in contemporary projects but not always. Doing one now that has a stretch with a bit set between two standard height.

I have always thought it was 18 inches which is what we have now, seems about right for me at 5'5". I still have to have a stool to reach the upper shelf and the cabs over the fridge and double wall ovens.

I'm 5'3", and I put mine at 17". I can reach the first two shelves. Top shelf needs a stool.

We have 18inches so that wecan tuck the appliances under the uppers. I will say though that you should check code in your area. At one point I was noodling on lower height for one of the areas and the local inspector here in CA said that they enforce 18inches unless it is a continuous cabinet like a hutch or a pantry pull out. The space above the cooktop was 30 inches for code.

I have open shelves that are 16" from the counter by the sink, the cabinet above my coffee area is 18" and the cabinets above my baking area are a whopping 24" ! I love all three as they meet my needs in the specific area. That is the key..think about how you are going to use the cabinets and the countertop. I have a kitchen with 11 ft ceilings so I had a lot of space to fill . c