Values given for size and weight are typical of indicated batteries. Charge and discharge characteristics are quite distinct for each chemistry, so links to applications notes are provided above for most types. I wrote an article on my experience with Li-Po batteries that you might be interested in reading.

There are two categories of battery cells, Primary Cells and Secondary Cells. Here is the basic difference:

Primary Cells are not rechargeable (disposable).
Secondary Cells are rechargeable.

Worthy of note is the newest battery chemistry on the commercial market: Lithium Manganese (LiMn). This battery has all the advantages of LiPo and LiIon, only without the sensitivity to overcharging and heating that causes explosions. As you might expect, LiMn cells and battery packs are even more expensive that the already overpriced LiPo and LiIon varieties. I keep expecting prices to reduce as more and more consumer products use them, but as with printer ink cartridges, there does not seems to be any relief in sight.

(2005 data)

	NiCad	NiMH	Lead Acid	Li-Ion	Li-Polymer	Rechargeable Alkaline
Gravimetric Energy Density (Wh/kg)	45 - 80	60 - 120	30 - 50	110 - 160	100 - 150	80 (initial)
Internal Resistance  (mΩ) (includes peripheral circuits)	100 - 200 6V pack	200 - 300 6V pack	<100 12V pack	150 - 250 7.2V pack	200 - 300 7.2V pack	200 - 2000 6V pack
Cycle Life (to 80% of initial capacity)	1500	300 - 500	200 - 300	500 - 1000	300 - 500	50 (to 50%)
Fast Charge Time	1h typical	2-4h	8-16h	2-4h	2-4h	2-3h
Overcharge Tolerance	moderate	low	high	very low	low	moderate
Self-discharge / Month (room temp)	20%	30%	5%	10%	10%	0.3%
Cell Voltage (nominal)	1.25V	1.25V	2V	3.6V	3.6V	1.5V
Load Current*   -    peak   -    best result	20C 1C	5C 0.5C or less	5C 0.2C	>20C 5C or less	>20C 5C or less	0.5C 0.2C or less
Operating Temperature	-40 - 60°C	-20 - 60°C	-20 - 60°C	-20 - 60°C	0 - 60°C	0 - 65°C
Maintenance Requirement	30 - 60 days	60 - 90 days	3 - 6 months	not req.	not req.	not req.
Typical Battery Cost	5.0 (7.2V)	6.0 (7.2V)	2.5 (6V)	10 (7.2V)	10 (7.2V)	5.0 (9V)
Introduction	1950	1990	1970	1991	1999	1992

* "C" is a unit that specifies the peak current supply capability of the battery. Multiply the mAh rating by the "C" value to arrive at
   the peak current. For example a 1000 mAh battery with a 20C rating can supply a peak current of 20,000 mA = 20 A.