[paul.fr]

when you buy new rechargable batteries you have to overcharge them, otherwise they will not hold a full charge the next time. The develop a memory of their state of charge (or something like that).

how and why do rechargable batteries gain a "memory"

[another_someone]

You should never overcharge batteries, but some rechargeable batteries are likely to develop a memory effect if they are not fully cycled (taken to full charge, and allowed to run down to zero charge).  If you do overcharge a battery, many types of batteries are then likely to explode - so you definitely should not be doing that.

This is not true of all rechargeable batteries.

This is true of Nickel Cadmium batteries (which are now being phased out because of concerns over the disposal of cadmium), and to a slightly lesser extent with Nickel Metal Hydride batteries.

Lithium Ion batteries, which have been taking over from Nickel Metal hydride batteries have virtually no memory effect.

Lead acid batteries (as used in cars, and many power tools) not only do not need full cycle charge and discharge, but can be substantially damaged (at least insofar as forshortening their life) if allowed to ever fully discharge.

One of the other problems with Nickel Metal Hydride batteries is there tendency to self discharge (hence the need for a full recharge on initial purchase).  There are new types of Nickel Metal Hydride batteries now on the market that are supposed not to have such a serious self discharge problem (being able to hold about 70% of their charge for at least a year), and I am not sure how well these batteries also fare with regard to the memory effect.

[paul.fr]

You should never overcharge batteries, but some rechargeable batteries are likely to develop a memory effect if they are not fully cycled (taken to full charge, and allowed to run down to zero charge).  If you do overcharge a battery, many types of batteries are then likely to explode - so you definitely should not be doing that.

This is not true of all rechargeable batteries.

This is true of Nickel Cadmium batteries (which are now being phased out because of concerns over the disposal of cadmium), and to a slightly lesser extent with Nickel Metal Hydride batteries.

Lithium Ion batteries, which have been taking over from Nickel Metal hydride batteries have virtually no memory effect.

Lead acid batteries (as used in cars, and many power tools) not only do not need full cycle charge and discharge, but can be substantially damaged (at least insofar as forshortening their life) if allowed to ever fully discharge.

One of the other problems with Nickel Metal Hydride batteries is there tendency to self discharge (hence the need for a full recharge on initial purchase).  There are new types of Nickel Metal Hydride batteries now on the market that are supposed not to have such a serious self discharge problem (being able to hold about 70% of their charge for at least a year), and I am not sure how well these batteries also fare with regard to the memory effect.

I was thinking of mobile phone batteries, in particular. Their reccomended first charge is 18 hours, yet after that just 2! So i presume, this is an initial overcharge. or is it something else?

[Soul Surfer]

It is usually possible to charge batteries at a very slow rate continuously without damaging them
The chargers are designed to charge them quickly initially to about 90% of their capacity and then switch to a slow rate of charge that will not cause any damage after that  the long initial charge just makes sure that they get fully charged the first time.