Re: Standard batteries
Firstly, make sure you're using low-discharge-rate rechargeables (aka hybrid, pre-charged, or Enerloops after the company who introduced, or at least popularised, the tech). They don't give you quite as much energy capacity as a standard NiMH rechargeable, so they're not as useful in devices where you can take them off charge just before use, and then thrash them over the course of a few hours/days (e.g. using them to power a camera whilst taking photos all day at an event).
However, for devices like remotes, mice etc. where the device itself only sips energy from the battery bit by bit and where you're expecting a set of batteries to therefore last several months/years, their much lower self discharge rate means they retain significantly more of the stored energy for the device to use over that timescale, rather than (as with a standard rechargeable) throwing most of it away itself within the first few weeks after being taken off charge.
Secondly, once you've done the above, make sure your batteries come from reputable sources - don't just believe the headline capacity figures quoted by some of them. Whilst there's no need to pay the premium for well known brand names, you should be wary of going too far the other way and over-economising, ending up with batteries which may be some way removed from their advertised characteristics.
Thirdly, don't always believe a device when it's telling you the batteries are low if you're using rechargeables instead of alkalines - many devices base their low battery warnings on how alkaline batteries behave during use, i.e. the voltage across each battery dropping fairly steadily from 1.5V as the battery discharges, such that they might start to warn around a low battery level once the voltage drops to around 1.1-1.2V.
The problem here is that NiMH rechargeables only deliver around 1.2V when fully charged, but then hold a far steadier voltage almost up to the point where they're fully discharged, so some devices may flag them up as being "low" almost from the moment you fit them, even though they'll actually still work just fine for however long you were expecting them to work. e.g. based on how long it's been since my wireless mouse first started warning me about low batteries (it's running off a couple of low-discharge NiMH AA's), I'd be forgiven for thinking it must now be running on thin air given that I've yet to replace them...