While my refrigerator is not boxed in, I did have my GC extend the upper cabinet out to almost the edge of the fridge. I am fairly tall and use the space for cereal and cooking oils that I don't use every day. There is also a shoebox that has baking supplies in it like conf. sugar, baking powder, cupcake papers, etc. There is a lot of dead space in back but at least the front is easily accessible.

Here's our fridge/cabinet setup.

It sounds like yours is similar.
Our above fridge cabinet is also about 13".
We did't put any shelves in ours.
In it we keep oversize platters and commercial size rolls of plastic wrap and foil.
Some people install vertical dividers and keep cutting boards and baking sheets there.
Unfortunately, we found that our cutting boards wouldn't fit standing up so we moved them into the tall pantry cabinet to the left of the fridge.

For us, one side has the crockpot, George Foreman grill and odds and ends. The other currently has snack in it, but I want to figure out a better plan. I will put the vertical tray/sheet storage in another upper (the top part of the tall oven cab).
We only have uppers on our tall cabs and over our fridge and freezer. They are all wide and full depth and we are definitely not utilizing them enough. I am thinking of getting a rollout or 2 because there is no way to reach anything in the back.
OTOH, the back parts have made good hiding spots if the boys need their DS or other objects taken away. It could also work for Xmas/bday gifts because they would never think to look up in the back behind the things at the forefront.

Ours is 24" high and 24" deep (pulled out from the rear to make it flush with the fridge). We have one shelf inside, so each section has about 11-1/4" in height. The top shelf has the Foreman grill, the little crock pot and the big plastic cake carrier. The bottom shelf has the glass cake stand, the big mixing bowls and colander.

The cabinet came with another shelf, but we nixed it. We needed the storage for bulky things. Of course, it will all depend on what you need to store up there.

I had been planning one pullout and then putting things like a crockpot and thermoses that I rarely use towards the back. The pullouts are spendy so I didn't want to spring for two. My fridge choice changed so now I won't have a cab above. I already thinking I'll miss the hiding places that cab offered.

Yes, of course it will depend on what we need to store on top, but that's what's tough. Not sure til I get everything else put away. Working on that today. Kind of want a vertical divider so if I want, I can keep non-food, non-cooking stuff on one side if I like. I have a friend who slides all her son's work onto a shelf and then looks at all of it at end of school year to decide what to keep.I'm terrible with piles of paper elsewhere, so that was kind of appealing. I have 2 kids, so if one side of vertical is then in 1/2 horizontally, could slide one kid's stuff on one shelf, the other on other, and then still have other side of vertical divider for bulky cooking stuff, or extra food storage. But, putting in the vertical divider definitely limits putting in some other things. REally won't know how well I'll use the space til the whole kitchen's in action again and can see how we change our storage patterns overall.
We do have lots of vertical storage slots in a bottom cabinet, and we love that. So, don't need it so much over fridge. Was thinking more horizontal shelves over fridge for lasagna pan, breakfast tray, etc, but now thinking deep horizontal shelves might be tough to access if things slide backwards. Thanks for sharing your upper fridge storage!

I keep things like vases in mine. Another thing I've had up there was paper plates, plastic forks, etc for when we have BBQs and such.

Ours is divided into vertical and horizontal storage - 21" high, 26" deep, with one shelf. The shelf side stores extra stock pot, extra crockpot, popcorn popper etc. Shelf only extends half of depth which was the result of running out of material, but has made me very happy because I can store taller items in front.

We just finished our remodel and have a full cabinet over our cabinet depth fridge. Cabinet maker is going to make half of it a wine rack (2 shelves - 2 bottles deep) and the other half open for storage of large appliances (crock pot, roaster, pasta pot, etc.)

I like the idea of the horizontal shelf only being 1/2 deep... I think that might be a good way for things not to get lost in the back/bottom. At 13" not many sheet pans are going to fit vertically, and as you've said you have lots of vertical storage elsewhere. Just remember it will be hard to reach, so kids' art for looking at at the end of the school year will be okay, but permission forms for class trips will not!
Here's mine, but I'm blessed with luxury of 21" height. Now that I look at it though, the Rev-a-Shelf dividers are 12" high, and most things don't extend beyond them, so you could use some for vertical storage if you chose... maybe I actually need to think about a horizontal shelf since I'm not making use of all that space! :)

I'm going from the less depth cabs in the old kitchen to to full size in the new. It is boxed in but nowhere as nice as willtv's (that is gorgeous) I'm not quite sure if I like it or not. May take some getting used to. I put items infrequently used up there, extra large plastic Tupperware, crock pot, snd of course the really good "hootch" (the good stuff only used for special occasions). I like the the idea of the wine rack.

Use it for a flat screen in the front and then have a sideways pullout to access the back areas. Or put an "upside down" rollout up high with wine glass holders on it to hang glasses from it and a rollout wine bottle holder at the bottom. I had a client who used vertical dividers to store wrapping paper for half and put a tote for the scissors, tags, and cards in the other half.

A lot will depend on what ends up with no home elsewhere.

I *have* a cabinet above my CD fridge. I think there are vases in there. I can't reach it, so whatever's in there is only accessible via human step-ladder (meaning my tall son and tall husband).

I don't even keep long-term stuff in there--it's easier to keep stuff in the basement than to get it out from that high.

I do use the space above the ovens though!

My over-fridge cabinets come all the way out to the front of the fridge and all the way back to the wall, so they are deep. No shelf. We keep the crockpot up there, and lots of bottles of liquor (which we hardly ever use as we mostly drink wine which is stored elsewhere) and some other random stuff. I'm 5'11" and even so I need to stand on a chair or stool to reach things that are more than halfway back. Now I'm getting curious about what is actually lurking back there...

Mine's about 32W x 18H x 26D (interior dimensions). It has one full horizontal shelf. I use it for large platters and other large, shallow serving pieces that I don't use often and that don't fit in a regular depth cupboard. I stack them with bubblewrap between them. It has been a good use of space that is more difficult to access. I prefer getting out the step stool, which hangs in the broom closet around the corner, to walking down to the basement. Actually, the platter I use most is accessible even without a stool - and I'm only 5'3".

Mine is above a CD fridge and is 36" wide. I have storage like CO-Co with 6 vertical racks and I love how much stuff I have in there. Cookie sheets, cooling racks, casserole dishes, broiler pans, all my cutting boards, grill rack. A very efficient use of space.

Thanks for all the pictures of your over fridge cabinets. I think we've decided to put one long horizontal shelf on bottom of cabinet, with a long verical divider between it. That still leaves a pretty big space above the horizontal shelf. Cabinet maker said it will be no problem for us to remove this and change the shelving if we decide this doesn't work. So, we need to stop worrying about "perfect" solution! It really will be hard for us to know how we'll use this space til we've put rest of items away in other cabinets. We will actually have a lot of new space way up high in upper cabinets over regular cabinets since we had cabinets built to ceiling. It won't be super easy to use (and if I'm here til I'm "old" I'll probably never get to them!), but I can reach all with a step stool, and because I'm so short (5 feet) I pretty much assume I need a step stool even for top shelves on regular cabinets. I did insist that our baking center have upper cabinets that come down lower than standard, just for me!

I like the ideas for hiding presents in the space! This gets harder as the kids get older!