I'm converting a decorative windmill to a power generation device. I'm looking for a battery that can charge with wildly different voltages and currents and be simple and easy to charge. It doesn't have to be "plop-right-in" simple, I'm perfectly willing to do some work to get it to work.
I don't think there's a battery that's quite that versatile (supercapacitors arn't batteries but may be good enough, it depends on what you want to do), but a Deep cycle Lead Acid may be worthwhile. Lead Acids can take a bit more abuse than some chemistries (Lithium) and the chargers for them have almost nothing in them (well the cheap ones anyway) beyond something that prevents reverse power flow (which'd drain the battery) and something to limit the peak voltage to 14.2-14.6V or so. A diode and a voltage regulator will probably do (unless you want to get fancy and go with a 3 state Lead Acid smart charger). The charging current for any battery can be just about anything from near zero up to whatever it's rated to handle, it's the voltage that's going to be the real issue. If you've got REALLY wild supply voltages, you might need a buck-boost regulator to give you a more manageable output voltage range.