Rechargeable batteries in standard household sizes have been on the market for decades they all have their problems. NiCd had issues with chargers and the misunderstood memory effect. Rechargeable Alkaline can't fully recharge, is limited in number of charge cycles, and usually fails by leaking. Traditional NiMh has a self discharge problem and charging is not convenient.
A new technology arrived in the past decade that changed the way rechargeable batteries are used. It has the power density of NiMh, it has low self discharge (although not as low as Rechargeable alkaline), and smart chargers prevent the charging issues of the NiCd era. What is this technology? It's actually NiMh! Low self discharge NiMh cells were introduced by Sanyo under the Eneloop name in 2005 (now made by Panasonic) and other companies soon followed.
What does this mean in terms of usability? It means a few things, firstly these cells are sold with a partial (approx 70%) charge so they can be used out of the package without recharging first. Instant usability was a major advantage of Rechargeable Alkaline. It is still NiMh technology which means the ability to handle heavy loads is still there. The mass availability of smart chargers eliminates the overcharge problem of NiCd. Of course the memory effect never occurred in consumer applications anyway (but was the blame of other issues, namely overcharging). The only two disadvantages that remain are to make sure people don't throw them away in error and that you don't have the full 1.5 volts.
This new technology means a major change in how the cells are used and stored. Low self discharge cells can be stored charged in battery organizers, ready to go, and used cells can then be stored in another organizer full of cells ready to be recharged (hint, put the used ones upside down in the same organizer to easily determine which ones need recharged). The instant availability of spare cells isn't the only game changer.
This new technology can also be used in equipment that stands by waiting for emergencies or even low drain devices such as clocks. Just make sure you check for voltage compatibility in clocks and older radios. My 1970s Panasonic transistor radio is a wonderful set, but it won't work for long on NiMh of any type. This means you can use these cells in your pre-staged emergency flashlights, just remember to top off the charge from time to time.
Now, in order for this to work well, you need good cells and good chargers. I recommend chargers with negative Delta V termination with single cell channels. Chargers that have two cell channels (require two cells to charge) are okay for anything used in Multiples of 2.
For specifics, I recommend Panasonic's Eneloop chargers for AA and AAA sizes and Tenergy's T-9688 for AAA, AA, C, and D, but not 9V. In fact I don't recommend NiMh for 9V, but I'll get to that later.
For cells, I recommend standard Panasonic Eneloop AA or AAA, don't bother with the Eneloop pro, the extra capacity reduces overall lifespan too much. The standard Eneloop can be recharged 2100 times where the Pro can only be recharged 500 times. If you don't mind the Capacity loss, you can also get Eneloop Lite which can be recharged 3000 times. There are other brands including the Tenergy Centura I recommend for C and D, but be sure you don't get cheap, low capacity types (pay attention, especially when buying the big brands).
For C and D size I recommend Tenergy Centura. This is because this is only other reputable brand I found with good capacity. In these sizes I highly discourage the big name brands, Energizer only goes up to 2500 mAH (which may not even be Low Self Discharge) and Ray-O-Vac up to 3000 mAH. These are near or slightly better than AA. Tenergy is around 4000 mAH for C cells and 8000 mAH for D-Cells.
For 9-Volt size I do not recommend NiMh as smart chargers for this size are difficult to find. In addition 9-Volt is rather complex. A Carbon Zinc or Alkaline 9-Volt has six cells. For a NiMh based battery to have the best compatibility more cells are needed. Six cells gets 7.2 volts, but the better types have seven cells for 8.4 volts or eight cells for 9.6 volts. The more cells needed in the same space, reduces the amp-hour capacity. However, there is another way to reach 7.2 to 8.4 volts with different technology. Two lithium Ion Cells in series will produce 7.4 volts nominal, but with 8.4 volts at a full charge. Lithium ion offers a few advantages, even lower self-discharge, good voltage compatibility, and even more power. In addition, lithium Ion charging requires a smart charger and in this case, probably a balancing circuit inside the pack as well.
The last question I need to answer is what you should do where you can't use NiMh cells for reasons of voltage compatibility, safety certification, internal charger compatibility, or for safety equipment (smoke detectors). If the issue is voltage compatibility, the best answer for AA, AAA, and 9V types is to either continue using standard cells that you normally buy or switch to Lithium. The lithium type will allow you to retain the reduction of leak risk that NiMh provides. If the issue is safety certification (unlikely in household use), you must follow the requirements of certification. Some equipment may allow you to use other types and simply change back to the permitted type to restore certification. Internal chargers can either be disabled as for Alkaline or not used, if neither is an option, NiCd cells are still available in the US. Lastly, I don't recommend rechargeable batteries for smoke detectors as most types state not to use them in the manual. For these I recommend a lithium replacement or if the detector is near end of life, replacing with a 10 year sealed battery type.