There is no agreed-upon definition of "counter-depth". It may be the depth of the refrigerator box (i.e., without the doors) or it may be the depth of the entire refrigerator. Also, you didn't specify a width, finish, or any other requirements.

Yes, it absolutely would help to know a few more details. Available dimensions, budget range, desired features, and expected visual appearance all matter.

We have a 36" SubZero all-fridge. We picked this model, as we have had great luck with SubZero before and they have a reputation of lasting for several decades with only minor repairs. They also have an air treatment system that works quite well at keeping food fresh for longer, and they are very good about chilling very evenly so that there are no unexpected cold spots. We like the interior organization. And we love that it doesn't have things like ice makers nor through-door appliances; those waste space and energy and are prone to breaking more frequently.

SubZero makes counter depth fridges that can be made to look just like another cabinet, or there is another version of their fridges that can be built into a cabinet with a door that stands just proud of the front of the adjacent cabinets. If you have extra deep cabinets you can also recess the latter version back by a few inches and the door becomes flush with adjacent cabinets. But it won't look exactly like a cabinet door. It looks like an appliance. So, you have options here. Other manufacturers might not give you this choice. Usually, the less expensive models all require that the door stands proud, and the more expensive models have special hinges that allow flush mounting.

Many people decide to put cabinet panels on these type of fridges, but you can also order them with stainless steel fronts. You typically need to buy your own cabinet pull for these type of installations; so factor that into the cost. Big fridge pulls can end up costing hundreds of dollars depending on the design that matches your kitchen.

And that's really the major downside here. It doesn't get much more expensive than SubZero. So, that's why I said we need a budget range in addition to the list of desired features.

We bought Whirlpool S-b-S counter depth almost two or three years ago. Slightly better reliability per CR magazine and Lowe's had it in stock when the older fridge died. It also fit under the cabinet above the fridge. (Measure!) So far it is doing well.

SZ also offers side panels for free standing use with their designer series, which is what we got for our freezer. Yes, the unit has to be anchored to the wall, but it doesn’t need custom cabinetry.