I just purchased a new Kodak Digital Camera which includes a
rechargeable Lithium battery. Ni-MH batteries are an optional
accessory at an additional cost. I believe one type must be be
recharged only when it is completely drainged, while the other may be
recharged at anytime (like a cell phone battery). Which is which? Any
suggestions on which type is better also appreciated.

Hello Chance0110

I recently had a similar option when buying my new digital camera and
decided to buy the Ni-MH batteries but this was mainly on cost
decision.  I have found that separate recharging units were easier to
buy for Ni-MH batteries as were the batteries themselves and I now
always carry a spare set of batteries with me (and the charger if I am
on vacation).

Nickel Metal Hydride (NiMh) can be recharged quickly and easily, do
not suffer from "memory effect" and do not need to be fully discharged
before recharging.

Lithium Ion (Li-Ion) batteries are the most advanced technology and do
not suffer from "memory effect", do not have to be fully discharged
before recharging, and deliver more energy per charge than NiMH or
Ni-Cd chemistry batteries.  Li-Ion batteries also tend to be more
expensive to buy and replace.

Nickel-Cadmium (Ni-Cd) batteries must be fully discharged before use
and are prone to "memory effect".

"Memory effect" is the reduction in total capacity of the battery,
this occurs each time the battery is recharged.
 
My recommendation would be to forget Ni-Cd batteries (they are too
old-fashioned!) and go for Li-Ion or Ni-MH.  In the end it comes down
to simple economics, if you have the money buy a Li-Ion replacement
(and charger) if not get the Ni-MH.

I hope this answer is helpful.  If you require anything else on this
subject please ask for clarification and I will do all I can to help.

Useful links:
http://www.greenbatteries.com/documents/Battery_FAQ.htm
http://www.greenbatteries.com/documents/battery_myths.htm
http://www.greenbatteries.com/documents/Battery_Charger_FAQ.htm
http://www.valence.com/faq.asp?topic=lithium

Excellent answers. Thank you so much!

Hi chance0110-ga,

  In addtion to the views by palitoy-ga, I would like to share my
opinions on the same, and hope it helps you in making the right decision:

i) Although NiMH batteries work as well as or better than the Alkaline
batteries they replace, they tend to provide less operating time due to the
reduced cell voltage(1.25V versus 1.5V for the alkaline).  This is not
the case, if the manufacture recommends using NiMH, which means the
reduced voltage provided by NiMH is taken into consideration during the
design of the camera.

ii) NiMH batteries have much lower internal resistance that enables them
to drive the power hungry digital cameras(mainly due to the TFT screen,
rapid flash charging, fast motorized zoom) without any problem.

iii) NiMH batteries do have higher rate of self discharge(means that the
battery gets discharged even if you don't use them over a period of time).
This depends on the storage temperature/humidity. You could use a freezer
safe ziplock bag with some humidity absorbing silica crystals, to overcome
this limitation(but make sure you allow sufficient time for the batteries 
to warm up before use). It might be better to carry backup alkalines for
emergencies.

iv) The main advantage of the NiMH is the availability and the compatibility
with existing alkalines. You could easily buy a NiMH battery anywhere compared
to a proprietory LiIon battery, and also easily substitute one with a
alkaline battery incase of emergencies(when the battery is not fully charged,
dies half way etc.)

v) There is an exception to the suitability of the NiMH, when it comes to the
high performance high resolution cameras(above 5.0Mpixels). LiIon does a better
job in these cameras, due to its relatively low internal resistance and the
ability to handle sustained high discharge rates.

I totally agree that NiCd batteries are unsuitable for digital cameras, due
to memory effect and poor storage/discharge capacities.

Regards
ldavinci-ga