Is it a good idea to use NiMH rechargeables in place of ordinary disposable alkaline batteries?
The general answer is "yes" because using rechargables results in less going to landfill, fewer annoying trips to the shops for replacements, and less face-palming when Johnny accidentally leaves a gadget on flattening the batteries — just recharge!
While NiCd (NiCad / Nickel Cadmium) cells and batteries have fallen out of favour because of the toxic cadmium metal that can seep out in landfill, NiMH batteries are considerably more benign.
NiMH batteries can outperform normal disposables such as "alkaline" cells, with higher capacity.
Normal NiMH batteries have a fairly high self-discharge, ie may run down in a few months even if not used, but the newer low-self-discharge (LSD) style such as Maplin's "hybrid" range though more expensive and usually slightly lower capacity, can retain 80%--90% of their charge after a year, and so are often supplied charged and ready for immediate use.
The newer low-self-discharge NiMH batteries can be eye-wateringly expensive, maybe three or four times the cost of a disposable set but are good for about 1000 charges.
Ordinary NiMH rechargeables can be quite competitive with alkalines on price, and generally with a 1000-cycle life too.
You will need a dedicated NiMH charger, but with even a clever one that can charge AAA/AA/C/D/PP3 sizes not costing much more than a set of batteries, you're ahead money-wise after only a few charges since mains power to charge them is essentially free for example.
(If you're feeling particularly sophisticated then you may be able to charge your NiMH batteries directly from, for example, a 12V off-grid solar PV system, using a charger designed to run in-car.)
NiMH is likely to be especially economical for high-drain items, or things that may get left on by accident such as torches or toys.
I have only encountered a few devices that are not happy with the lower voltage of NiMH cells (1.2V) compared to typical disposables (1.5V), and if you need to keep on using them then you'll still need a few disposables.
In the case of something like a smoke alarm, an appropriate low-self-discharge battery (eg PP3/9V) may cost more than the unit itself, and outlast it with an annual recharge keeping it going. As an experiment I have 2010/12/28 just put a Maplin "hybrid" PP3 (part N92GK) in a fire alarm that had previously contained an alkaline, and I'll keep an eye on how long it lasts between charges. A recharge can be done during the day, so we need not ever be without the alarm active while we sleep. (It still seemed to be going strong 2011/09/09 when I had to recharge the non-hybrid NiMH in our other smoke alarm.) Both alarms started emitting warning beeps in the wee hours of 2012/05/04! LFB installed new free smoke alarms (without replaceable batteries) 2012/09/12 during a requested fire-safety visit so this test is over; neither alarm was complaining about low batteries before the replacement.