I have recently purchased a new digital camera which uses
re-chargeable batteries. I have not used rechargeables for 10
years and have the following questions:

The battery pack says charge for 16-20 hours. Will I damage them if
they stay on charge for, say, 3 days or more ?

That depends entirely on the charger - not battery. So you'd need to
look at the instructions for that. If it obviously switches off after
charging it should be ok.

Wrong! It depends on both. You need to use a charger designed for the type
of battery you wish to charge. For example Ni-Cad cells need a quite
differnt charging patter than say Li-Ion ones.

Is it advisable/necessary to use/discharge the batteries totally
before recharging, or can I recharge them when they are half used.
They used to say that rechargeables developed a "memory" - is that
still true?

It never was. It was a con to persuade you it was your fault batteries
didn't last.

Wrong! It was not a con at all, but has been repeatedly proven by
experiment. Ni-Cad cells are particularly prone to this.

I've seen advertised charges that will recharge ordinary
non-rechargeable batteries. Are these any good ?

Wrong again!

They do work but not very well. Not a good choice really unless you are
desparate.

No. And rechargeables cost so little more anyway.

Wrong! Unless of course you regard a price difference of at least 50% as
being insignificant.

Peter Crosland