Technically speaking, no. Lithium-ion batteries cannot be overcharged. Once a full charge is reached, this type of battery will not accept any further energy. However, keeping such a battery plugged in and charging for an extended period of days can cause stress to the battery and, in the worse-case scenarios, trigger a fire or explosion.
Nickel Based Batteries
Nickel-metal-hydride batteries are similar to lithium-ion; they cannot accept an overcharge and trickle charges must be kept low to avoid safety hazards.This type of battery is non-toxic and offers a higher specific energy than nickel-cadium.
The nickel-cadium battery was invented in 1899 by Waldmar Junger. Two waves of improvements were made subsequently, first right after World War II with casing technology and then in the 1980s when capacity was upped by around 60%. There are many claims on the Internet that leaving a cell phone battery plugged in overnight on a continual basis can permanently damage the power source. However, these claims are false. With few exceptions, a defective cell phone battery will have been caused by factory defect; not too much charging.
Conversely, some cell phone users may be doing themselves a disservice by never letting their battery completely die. Cell phone providers advise that at least once every couple of months, it is advisable to do just that.
Cell Phone Manuals
Despite all of the above, many instruction manuals for cell phone warn against overcharging. This is not because a battery can be overcharged per se, but because extended periods of incoming electrical charging may destabilize some of the battery cells.
In other words, once a battery reaches its full charge, it cannot be charged any further. At the same time, that electrical current that keeps coursing in has nowhere to go, creating a stressful electromagnetic environment and pushing the battery into more of an unknown realm. Depending on type, manufacturer and amount of time left plugged in, complications may or may not ensue.