Do you use them? Are they a pain to keep charged? Do they save tons of money?
The last set of Duracell AA NiMH 2650 mAh batteries I bought impressed me. The high capacity of these cells reduced the impact of the slow constant drain of NiMHs. I bought 8, so I could use 4 in my camera while I charged the other 4. With older, smaller capacity cells, I needed to keep 12 or 16 in circulation so I never ran out of juice.
If you use your battery operated device frequently, rechargeable NiMHs are the way to go. If you only use it on occasion, go with Lithiums, that are not rechargeable, but do not lose their charge over time.
They don’t work, and they’ll make you sterile. Avoid at all costs.
Well, crap.
I was hoping to utilize one of these or these. You’ve spoiled my fun. 
How long do these things stay useful for? How many charges will they take on average?
If you use a digital camera, you pretty much have to get NiMH batteries. Alkalines don’t last and Lithiums are only needed in extremely cold weather. Buy a good quality slow charger, 4 or 8 2500+ mAh batteries, and you can operate for a long time. They take 100’s or even 1000 charges, but they do drain between usage. I tend to charge up the night before I plan on using the camera.
I also use them in my bike flashlight and some wall clocks.
One area where rechargeables are widely used is model aircraft. The reason is that NiCds, NiMHs and LiPolys can all bang out a huge current - LiPolys have to be babied lest they catch fire, but a modest-sized pack can still provide 20 amps for a few minutes. The cells all have a much lower internal resistance than a dry battery, and besides, who wants to replace half a dozen Duracells after five minutes’ use?
This application pushes the batteries to their limit, of course - they’ll last only a few hundred cycles with this kind of abuse. Still, the power to weight ratio is the reason why electric flight’s come along a lot in recent years.