If stocking up for any long term emergency, whether simply a blackout or something more serious, cost can be a consideration if large stocks are required.
It should be noted that AAA cells cost about the same as AA but contain only about the half the energy. The reduced weight may make the cost penalty acceptable for long distance backpacking, but not perhaps for home use.
D cells contain about 8 times the energy of AA for only about twice the price.
I would therefore allways prefer D cell flashlights, lanterns, and other appliances for longer term use.
The humble D cell Maglite gives 12 hours good light on Alkaline cells, this may be greatly extended by fitting a lower powered incandescent bulb or an LED.
Remember that in an emergency popular batteries may be unobtainable, but the more obscure ones might still be available.
Therefore IMHO prudent preps should not only include qaulity flashlights to take your prefered battery, but also some cheap lights for every type of battery you can think of!
I have flashlights or lanterns to take
AAA, AA, C, D, CR123, PJ996, AD28, and others.

Remember also that in some climates, heat can kill, not just cold, anywhere warm a couple of battery fans would be a prudent prep. I believe that these can be purchased in the USA but here in the UK I made my own. Run time is about 24 hours on 6D cells.

I also made some D cell LED lights that run for 1,000 hours on 3 D cells, these are not that bright but enough for safe movememt.
A case of 50 D cells would provide basic essiential lighting for 10 years with these LED lights.

Hmnnn, I think obscure batteries that are hard to obtain in regular circumstances are not going to be any easier to obtain during an emergency. And one hopes that you've already stocked up on batteries in advance. (I certainly have!)

Now, if you modded a 6 D cell MagLite to take a 9V Cree, you'd have my attention. (And you could probably cook with that thing too, so it does double duty.) But a regular MagLite is a something of a joke compared to a modern 2xAA flashlight.

I do have a number of D's stocked up for radio usage but I found it fairly trying keeping every kind of battery around the house. Much easier when you can share them among devices.

P.S. For completeness sake, it should be noted you can buy 8,000 mAh rechargeable D cells, but you'll have to get a special recharger for them and they are expensive.

My thought is I don't want to be trying to stock up when somehting happens, I want as much stock as I can. Lets say I have room for 200 batteries, if I have to stock AA, AAA, 123, C, D then thats only a handful of each, but if I standardize on AA then I can stock 200 AA's.
Another thing is unregulated lights can utilize batteries which are too low to run in more complicated electronics. pop the "dead" battery from the radio and into the led light for a few more hours.

If still have a few C or D cell powered equipment and want to standardize on AA's, you can simply buy simple adapters, so AA's can fit in to C or D cell equipment.

I'm going to pick up a few of those adapters before next summer. I have a couple D powered items like the little air pump for the coleman mattress. That gets used once or twice a year and I always end up putting new D batteries in at the beginning of a year then pulling them out so they don't leak or the switch get bumped on. I could toss a set of rechargeables in and be done with it.

Sounds like a good idea, but as I'm sure you know, you'll only be getting 2100-27000mAh rather than 8000-12000mAh out of each "D" cell. But I'm guessing that should probably be enough for an air mattress motor.

In the last big blackout in Somerest, England, AAA, AA,C, and D cells were in short supply from retailers.
The local electrical trade supplier had ample stocks of AD28 batteries, of "door bell" batteries,electric fence batteries, and very expensive 3.7 volt LITHIUM D CELLS.

The local pub was lit by a variety of lights that I loaned them, mainly kerosene pressure lanterns, and small 6 volt incandescent bulbs worked off electric fence batteries.

As you point out it would have been prudent to stock up first, and I had done so, but others were less well prepared.

Thats ok, because the mattress motor doesn't need to run that long, its never run the batteries down, I usually misplace them by next year or stick them in something else.
I've noticed a lot of store bought rechargeable D batteries are the same capacity as AA also, to get the full capacity you have to order them from a reputable brand, i.e. no energizer, duracell, etc that are trying to hit a walmart price point.

I've ordered two (2) 2D-packs of Energizer rechargeables for my Maglite after reading some favorable reviews. Just as they're about to arrive, this thread pops up. Now I don't even know if i should open them or try to sell/trade off...

Super.

I stopped buying rechargeable batteries, I know the new Eneloop are supposed to be better, and it looks like they may be. But I’m going to give them at least another year then see how they hold up for holding a charge. I bought 4 packs of energizers (1 pack still sealed up) and the 3 packs I did open up were a very big disappointment.

I buy my alkaline AAs at Big Lots, they are made by Fuji Novel and they work as well as others. They are $1.49 for a 4-pack. And the “use by” date is always good. I’m looking at a pack right now and it is dated Jan 2014. So they are not old stock.