What is the difference between Nickel Cadmium(Ni-Cd), Nickel Metal Hydride(Ni-MH) and Lithium Ion(Li-lon) batteries?

Nickel Cadmium-Ni-Cd
Nickel Cadmium batteries may suffer from reduced run time if they are not discharged completely before being recharged. This is the so called memory effect which reduces battery life but can be reversed by completely discharging (Not to zero volts but 1 volt per cell. Running the device until it powers down is sufficient.) and recharging, sometimes over a number of cycles (at least 3 times). A more common reason for reduced life is overcharging by poorly designed battery chargers which continue to charge the battery rather than automatically shutting off and is not reversible. You can determine if this is occurring by checking if the battery is warm or hot sometime after the charger indicates a full charge.
Ni-Cd batteries use cadmium which is highly toxic to the environment if not disposed of properly. They have a life of approximately 500 cycles but in practice this is probably much less due to memory and overcharging.

Nickel Metal Hydride-Ni-MH
Nickel Metal Hydride batteries have an approximately 40% higher charge density and will run longer on a charge than an equivalent Ni-Cd. They do not suffer to the same extent from the memory effect and do not need to be fully discharged before recharging although occasional discharging may be beneficial. They have a life of approximately 1000 charge cycles.
Ni-MH batteries are a more environmental friendly alternative to Ni-Cd.

Lithium Ion - Li-Ion
Lithium ion batteries have the greatest charge density (60% higher than Ni-MH ) and do not suffer from memory effect. Although more expensive they offer longer use, lighter weight (30%-40% less than Ni-MH) and less self-discharge than other battery chemistries. They have a life of approximately 500 charge cycles. They are more environmentally friendly as they don't contain toxic materials such as Mercury or Cadmium.