Our fridge is at the end of a cabinet run and next to a doorway too. I think the decision of whether to go with counte depth would depend on how you would like for it to look and on aisle width. We have an island across from the counter and refrigerator and needed to go with counter depth to keep the aisle width sufficient. We also thought it would look better integrated with the rest of the kitchen.

My CD fridge is at the end of the run next to the doorway too. My kitchen is narrow, so I did not want the fridge to stick out any more than it had to. Mine has a panel which matches the cabinets on the side of the fridge, so this is what is visable as you walk into the kitchen. I don't think it was possible for me to recess the fridge with my kitchen.
I am not sure how to recess the fridge into the wall, but I have heard about others here on the GW who have done just that.
If you do not get an answer on this post, maybe post another question asking how to do so.

If you recess into the studs, you will get four extra inches (stud width is 3 1/2 inches, dry wall width is another 1/2 inch). You cannot do in on an external wall. As the previous poster indicated, if the wall is load bearing, you will need to build and install a header joist in order to remove the necessary studs. Removing the studs will likely cause damage to the other wall (for the adjoining room) which will need to be repaired. Also, since you have removed the wall and (if any) insulation, the refrigerator may be noisy in the adjoining room. Finally, you may find that there is other stuff in the wall that has to be relocated, such as HVAC ductwork or electrical wiring. Some of this is relatively easy to do, while others are virtually impossible.

We have a CD refrigerator at the end of a short run of cabinets in our small U shaped kitchen. We wanted to save as much space as possible and were not able to set a regular refrigerator into the wall. We also used a shallower side panel on the ref. because of a dark corner on the other side of the refrigerator and the GE Cafe CD because it had SS side panels that would show. We did widen the door in to the DR which made a big difference visually.

Our refrigerator is on the end of a run in a doorway as well. But, since we have a narrow aisle at that point and our refrigerator is on an outside wall (so no recessing), we went with a counter-depth to save aisle space.
As to how to recess into the wall, others have described it pretty well. What isn't mentioned is that some people recess their refrigerator not only into the wall, but into the room behind it. If you need to recess your refrigerator more than 3" or 4", you will need to recess into the next room. However, even those 3" or 4" can help if you have a standard depth refrigerator!
Since CD refrigerators are not totally counter-depth, they will stick out several inches beyond the surrounding counters...up to 3" or 4" for the doors and another 2" or so for the handles (depending on the refrigerator). The doors must stick out past the counters to open fully. Because of this, we also built our refrigerator in with end panels (end panels are only as deep as the distance b/w the back wall and the front of the refrigerator carcass/box).

Note that a full depth end panel will not make a difference in a "dark corner" b/c the refrigerator will be just as deep so will still create the "dark corner". I.e., whether you have full or partial depth end panels the effect will be the same b/c the refrigerator will be even deeper.

One more comment...how deep is the wall next to your refrigerator? If it's deeper than 24" or 25" you will need some filler b/w the refrigerator & the wall...the deeper the wall, the more filler will be needed. If it's no more than 24" or so, you shouldn't need any filler unless there's door trim...then you will probably need filler to clear the door trim.

Ours will also be at the end of a run, next to a doorway (well a 6' opening pass through into the dining room).

We had to get CD because we couldn't block the isle between the fridge and island, but also I really wanted to minimize any tunnel effect or feeling of blocking-off between the dining room and kitchen. I wish the fridge wasn't there at all cause it will hinder the view from each of the rooms into the other, but it was the best place for it.

I am using the CD right now and wish I would have given up my full depth years ago. We are a family of 4 who always has tons of food on hand, and I find that I actually have plenty of room, and it's so much easier to manage my fridge now. It's clean and organized - with just opening it I can "take inventory" in an instant - no more bottles or jars of food that sat hidden in the back for 2 years cause they either fell behind the shelves or just became a permanant placement. No more stuffing the fridge to overflowing cause I could. We use the fridge in the garage as backup. I love the organization that CD provides, and don't plan to go back to full depth ever again.