There are three major categories of rechargable batteries in retail trade, each with their own quirks. The three types are Nickel Cadmium (NiCad), Nickel Metal Hydride (NiMH), and Lithium Ion (Lithium). Oh yeah, there's also "rechargable" alkalines. Each type has its own charging scheme.

For a good basic understanding there's good information here. Rechargable batteries are called 'secondary batteries' while single use batteries are called 'primary batteries'. The section on rechargable lithiums seems to be missing tho.

The executive summary:
NiCd: Can have a 'memory', long shelf life, low power density, low cost
NiMh: Short shelf life, high power density, moderate cost
Lithium: Long shelf life, highest power densities, highest cost
"Rechargable" Alkaline: Long shelf life, high power density, limited charging cycles, moderate cost.

I hope this is helpful.

-Zeke