I used to have problems many years ago with a generator burning bulbs, especially once the first of the pair went.

Wondered if putting a battery in parrallel would help.
Would seem to have the added benefit of keeping the lights aglow when stopped.

If it's high frequency spikes that burn the bulb, would putting a low pass Resistor-Capacitor filter in parallel with said battery solve the issue?

First off you wouldn't connect a battery directly to the output without being sure it was designed for that. You would need some kind of a regulator circuit to adapt the changing generator output voltage to the charging requirements of the type battery you are using. And the battery in itself is essentially a low-pass filter to which the RC network would add nothing except loss and what 'high-frequency spikes' you talking about from a slow RPM DC generator? Without carefully matching the generator output to the specific battery you could under charge the batt rendering the whole project disappointing, or overcharging the batt reducing battery life and/or damaging the generator. Other for that it sounds like a good idea.

It depends on what the output of the generator is. The vast majority are AC output, which means you would first need to use a rectifier (4 diodes) to convert to DC. Most generators are 6 volt 0.5 amp rated, so a good match would be 5 1.2 volt nimh batteries. It should regulate the voltage reasonable well.

Some electric screwdrivers use only one diode to rectify AC current from a wall mount transformer for recharging the screwdriver's internal batteries. It is not real efficient because it wastes a good portion of the AC sine wave cycle, but it is cheap and it works. It would provide choppy current, which is better for battery charging, anyway. The four diode rectifier mentioned is called a bridge rectifier, in case anyone is unfamiliar with them and wants to search for an explanation on the Internet that would allow building one.

An electronics book I have says batteries in parallel with another DC source have the effect of regulating the voltage. I have not tried it, but it sounds like it would work.

I am not sure about how well a low pass RC filter would work to reduce spikes. It seems the spikes would be voltage spikes, not frequency spikes. RC filters usually reduce frequency spikes. You could always try it. All engineering principles were developed by trial and error at some point.

Bicycle generators are AC ? I always assumed they were DC with permanent magnets for the field.

I took one apart after it generated its last. Permanent magnets attached to the shaft spin. A thin piece of steel that looks like an asterisk has a web of wire for a coil laced around the arms of the asterisk out to about half of the length of the arms. At that point the arms bend upward inside the can that is the generator body. There is no commutator. Such a generator would just about have to be AC.

I remember having this problem also as a kid, and finally came to realize that my replacement bulbs were not rated for the voltage (6v, IIRC). I think I had 4.5v (3D cell battery bulbs) in place. You can get away with this for a while when two bulbs are in parallel, as their capacity exceeds the max current output of the generator. So as long as you 'load' down the current, the voltage stays in check. Once one bulb fries from the slight overvoltage, the second one gets the full blast, and cooks shortly thereafter.

Sounds like they have been misnomerred-if they are AC they should be referred to as alternators.

A low pass filter would cutoff spikes above a certain frequency. For a bulb, you just set a lower cuttof frequency.

I had a car alternator with worn bearings that was burning up voltage regulars from its voltage spikes due the play of the rotor. Thought the bulb burnouts were likely a result of the generator putting out spikes over the bulbs limits.

I had the correct bulb.