Can rechargable batteries get too old and can't be charged again?

I have several batteries for my Digital Camera that I recharge regularly? How often can you do this?
And does there come a point when they won't recharge?

You most certainly can wear them out. It just takes a long time. See, each time you recharge a battery, you are basically reversing a chemical reaction that happens inside by putting it's energy back in. Without going too deep into chemistry, I hope it's enough to say after a while these chemicals get "tired" of switching back and forth.

To help with the battery's longevity, most manufacturers suggest "Cycling" - every month or so of heavy use, less often for less used, you completely empty the battery by leaving the item on, and keep going until the device will not switch on. Then, fully charge the battery. This can help keep the reactions from going "Stale", but it won't keep them going forever.

It does take a while to get a battery to the stage where it won't hold much charge - most people will have upgraded their devices far before this time.

Yes, they can wear out.

You can complete flesh it by little DC bulb then recharge again it works fine

it depends on the technology of the battery for how many cycles it has. Some rechargeable batteries can be "shocked" and regain some life. But ultimately, none of them will last forever. Ni-Cad (nickel cadmium) is the worse. Ni-MH (nickel metal hydride) is next, and Li-ion(lithium ion) is the best.

Short answer - YES they get old and won't hold a charge well.

Nickel metal hydride (NiMH) batteries should be able to recharge somewhere between 500 to 1000 times. What you will see when they get older is that they won't have as much capacity - they won't last as long and you'll notice you have to change them out more often.

If you have lithium ion (Li-ion) batteries, there is one life factor that people are noticing. No matter how well you care for your battery, once it gets to be around two years old ( from manufacture date) the battery no longer holds a charge.

yes they will eventually either not take a charge or discharge very quickly.
the act oif charging and using them is a chemical reaction in the battery so at some point it is no longer able to do so.